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  • 1
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2249-2283 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper concerns a relationship between the kernel of the Bargmann transform and the corresponding canonical transformation. We study this fact for a Bargmann transform introduced by Thomas and Wassell [J. Math. Phys. 36, 5480–5505 (1995)]—when the configuration space is the two-sphere S2 and for a Bargmann transform that we introduce for the three-sphere S3. It is shown that the kernel of the Bargmann transform is a power series in a function which is a generating function of the corresponding canonical transformation (a classical analog of the Bargmann transform). We show in each case that our canonical transformation is a composition of two other canonical transformations involving the complex null quadric in C3 or C4. We also describe quantizations of those two other canonical transformations by dealing with spaces of holomorphic functions on the aforementioned null quadrics. Some of these quantizations have been studied by Bargmann and Todorov [J. Math. Phys. 18, 1141–1148 (1977)] and the other quantizations are related to the work of Guillemin [Integ. Eq. Operator Theory 7, 145–205 (1984)]. Since suitable infinite linear combinations of powers of the generating functions are coherent states for L2(S2) or L2(S3), we show finally that the studied Bargmann transforms are actually coherent states transforms. © 2002 American Institute of Physics.
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  • 2
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2306-2347 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We discuss in this article the canonical structure of classical field theory in finite dimensions within the pataplectic Hamiltonian formulation, where we put forward the role of Legendre correspondence. We define the generalized Poisson p-brackets which are the analogs of the Poisson bracket on forms. We formulate the equations of motion of forms in terms of p-brackets. As illustration of our formalism we present three examples: the interacting scalar fields, conformal string theory and the electromagnetic field. © 2002 American Institute of Physics.
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  • 3
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2348-2354 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We perform the Batalin–Vilkovisky quantization of Yang–Mills theory on a two-point space, discussing the formulation of Connes–Lott as well as Connes' real spectral triple approach. Despite the model's apparent simplicity the gauge structure reveals infinite reducibility and the gauge fixing is afflicted with the Gribov problem. © 2002 American Institute of Physics.
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  • 4
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2355-2362 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study self-dual multivortex solutions of Chern–Simons Higgs theory in a background curved space–time. The existence and decaying property of a solution are demonstrated.© 2002 American Institute of Physics.
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  • 5
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2363-2393 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We prove local existence and uniqueness of static spherically symmetric solutions of the Einstein–Yang–Mills (EYM) equations for an arbitrary compact semisimple gauge group in the so-called regular case. By this we mean the equations obtained when the rotation group acts on the principal bundle on which the Yang–Mills connection takes its values in a particularly simple way (the only one ever considered in the literature). The boundary value problem that results for possible asymptotically flat soliton or black hole solutions is very singular and just establishing that local power series solutions exist at the center and asymptotic solutions at infinity amounts to a nontrivial algebraic problem. We discuss the possible field equations obtained for different group actions and solve the algebraic problem on how the local solutions depend on initial data at the center and at infinity. © 2002 American Institute of Physics.
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  • 6
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2394-2422 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The scattering theory of Lax and Phillips, originally developed for classical wave equations, has recently been extended to the description of the evolution of resonant states in the framework of quantum theory. The resulting evolution law of the unstable system is that of a semigroup, and the resonant state is a well-defined function in the Lax–Phillips Hilbert space. In this paper we apply this theory to a relativistically covariant quantum field theoretical form of the two (or more) channel relativistic quantum field theoretical form of the Lee model. We show that this theory provides a rigorous underlying basis for the Lee–Oehme–Yang–Wu construction. © 2002 American Institute of Physics.
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  • 7
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2439-2465 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This work investigates some global questions about cosmological space–times with two-dimensional spherical, plane, and hyperbolic symmetry containing "well-behaved" matter. The result is that these space–times admit a global foliation by prescribed mean curvature surfaces, which extends at least toward a crushing singularity. The time function of the foliation is geometrically defined and unique up to the choice of an initial Cauchy surface. This work generalizes a similar analysis on constant mean curvature foliations and avoids the topological obstructions arising from the existence problem. © 2002 American Institute of Physics.
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  • 8
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2423-2438 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Technical results are presented on motion in N(〉4)D manifolds to clarify the physics of brane theory, Kaluza–Klein theory, induced-matter theory, and string theory. The so-called canonical or warp metric in five dimensions (5D) effectively converts the manifold from a coordinate space to a momentum space, resulting in a new force (per unit mass) parallel to the four-dimensional (4D) velocity. The form of this extra force is actually independent of the form of the metric, but for an unbound particle is tiny because it is set by the energy density of the vacuum or cosmological constant. It can be related to a small change in the rest mass of a particle, and can be evaluated in two convenient gauges relevant to gravitational and quantum systems. In the quantum gauge, the extra force leads to Heisenberg's relation between increments in the position and momenta. If the 4D action is quantized then so is the higher-dimensional part, implying that particle mass is quantized, though only at a level of 10−65 g or less, which is unobservably small. It is noted that massive particles which move on timeline paths in 4D can move on null paths in 5D. This agrees with the view from inflationary quantum field theory, that particles acquire mass dynamically in 4D but are intrinsically massless. A general prescription for dynamics is outlined, wherein particles move on null paths in an N(〉4)D manifold which may be flat, but have masses set by an embedded 4D manifold which is curved. © 2002 American Institute of Physics.
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  • 9
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2466-2485 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper is devoted to the investigation of global properties of prescribed mean curvature (PMC) foliations in cosmological space–times with local U(1)×U(1) symmetry and matter described by the Vlasov equation. It turns out that these space–times admit a global foliation by PMC surfaces as well, but the techniques to achieve this goal are more complex than in the cases considered in Paper I [Henkel (2002)]. © 2002 American Institute of Physics.
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  • 10
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2505-2517 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general notion of bi-quasi-Hamiltonian systems is introduced and is related to previous work on various special cases of such systems. © 2002 American Institute of Physics.
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  • 11
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2814-2816 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We give a necessary and sufficient condition for the reality of the spectrum of a non-Hermitian Hamiltonian admitting a complete set of biorthonormal eigenvectors. © 2002 American Institute of Physics.
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  • 12
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2817-2830 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Compatibility relations in effect algebras and their connections with refinements of the orthogonal partitions of unity are studied. Properties of blocks as maximal sets of compatible elements are discussed. Some special kinds of effect algebras are characterized using properties of compatibility. Using refinements, an additional structure on the effect test spaces is introduced and used to a characterization of different types of effect algebras. © 2002 American Institute of Physics.
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  • 13
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1906-1915 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The generalized Hénon–Heiles Hamiltonian H=1/2(PX2+PY2+c1X2+c2Y2)+aXY2−bX3/3 with an additional nonpolynomial term μY−2 is known to be Liouville integrable for three sets of values of (b/a,c1,c2). It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton–Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions. © 2002 American Institute of Physics.
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  • 14
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1916-1937 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider a real Lagrangian off-critical submodel describing the soliton sector of the so-called conformal affine sl(3)(1) Toda model coupled to matter fields. The theory is treated as a constrained system in the context of Faddeev–Jackiw and the symplectic schemes. We exhibit the parent Lagrangian nature of the model from which generalizations of the sine-Gordon (GSG) or the massive Thirring (GMT) models are derivable. The dual description of the model is further emphasized by providing the relationships between bilinears of GMT spinors and relevant expressions of the GSG fields. In this way we exhibit the strong/weak coupling phases and the (generalized) soliton/particle correspondences of the model. The sl(n)(1) case is also outlined. © 2002 American Institute of Physics.
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  • 15
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1875-1905 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Motivated by the difficulty in using the splitting matrix method to obtain parabolic approximations to complicated wave equations, we have developed an alternative method. It is three dimensional, does not a priori assume a preferred direction or path of propagation in the horizontal, determines spreading factors, and results in equations that are energy conserving. It is an extension of previous work by several authors relating parabolic equations to the horizontal ray acoustics approximation. Unlike previous work it applies the horizontal ray acoustics approximation to the propagator rather than to the Green's function or the homogenous field. The propagator is related to the Green's function by an integral over the famous "fifth parameter" of Fock and Feynman. Methods for evaluating this integral are equivalent to narrow-angle approximations and their wide-angle improvements. When this new method is applied to simple problems it gives the standard results. In this paper it is described by applying it to a problem of current interest—the development of a parabolic approximation for modeling global underwater and atmospheric acoustic propagation. The oceanic or atmospheric waveguide is on an Earth that is modeled as an arbitrary convex solid of revolution. The method results in a parabolic equation that is energy conserving and has a spreading factor that describes field intensification for antipodal propagation. Significantly, it does not have the singularities in its range-sliced version possessed by many parabolic equations developed for global propagation. We then discuss two extensions of the method; first to propagation along refracted geodesics and second to a description involving discrete, local, normal modes.
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  • 16
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1938-1955 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The system of evolution equations for general motion of surfaces in orthogonal coordinates is analyzed to reduce the number of variables as well as equations. The explicit expression of the Lund–Regge surface is obtained. When the surface corresponds to the Lund–Regge equation, we prove that some components of velocity satisfy the linearizations of the Lund–Regge equation. The soliton solution is derived and one special case of the Lund–Regge surface is studied. © 2002 American Institute of Physics.
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  • 17
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    Journal of Mathematical Physics 43 (2002), S. 1237-1246 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the lowest energy E of a relativistic system of N identical bosons bound by harmonic-oscillator pair potentials in three spatial dimensions. In natural units (h-dash-bar)=c=1 the system has the semirelativistic (or "spinless-Salpeter") Hamiltonian, H=∑i=1Nm2+pi2+∑j〉i=1Nγ|ri−rj|2, γ〉0. We derive the following energy bounds: E(N)=minr〉0[N(m2+2(N−1)P2/(Nr2))1/2+(N/2)(N−1)γr2], N≥2, where P=1.376 yields a lower bound and P=〈fraction SHAPE="CASE"〉32 yields an upper bound for all N≥2. A sharper lower bound is given by the function P=P(m) which makes the formula for E(2) exact: with this choice of P, the bounds coincide for all N≥2 in the Schrödinger limit defined by m→∞. © 2002 American Institute of Physics.
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  • 18
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    Journal of Mathematical Physics 43 (2002), S. 1340-1352 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we study the large Nc limit of SO(Nc) gauge theory coupled to a real scalar field following ideas of Rajeev [Int. J. Mod. Phys. A 9, 5583 (1994)]. We will see that the phase space of this resulting classical theory is Sp1(H)/U(H+) which is the analog of the Siegel disk in infinite dimensions. The linearized equations of motion give us a version of the well-known 't Hooft equation of two dimensional quantum chromodynamics. © 2002 American Institute of Physics.
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  • 19
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    Journal of Mathematical Physics 43 (2002), S. 1519-1535 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Some areas of modern theoretical physics such as modern cosmology contain different manifolds which must be glued together along a common boundary. These boundaries can be spacelike, timelike, or lightlike hypersurfaces. This paper shows how this gluing for different hypersurfaces is possible. Two different approaches are considered and the extent to which these approaches are equivalent are discussed. In particular, we will construct a distributional approach for dynamics of lightlike hypersurfaces in general relativity. Since Einstein's equations are nonlinear PDEs, for discontinuous metrics such as signature changing metrics, product of distributions are unavoidable. To glue two different manifolds which admit signature change, we consider this problem in the context of Colombeau's new theory of generalized functions. Some examples are given for clarification. © 2002 American Institute of Physics.
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  • 20
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    Journal of Mathematical Physics 43 (2002), S. 1547-1568 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The expressions for 12j coefficients of the both kinds (without and with braiding) of the SU(2) group and the quantum algebra uq(2) are considered. Using Dougall's summation formula of the very well-poised hypergeometric 5F4(1) series and its q-generalization, several fourfold sum formulas [with each sum related to the balanced 5F4(1) or 5φ4 series] for the q-12j coefficients of the second kind (without braiding) are derived. Applying q-generalizations of rearrangement formulas of the very well-poised hypergeometric 6F5(−1) series [which correspond to a new expression for the Clebsch–Gordan coefficients of SU(2) and uq(2)], the new expressions with five sums [of the 4F3(1) and 3F2(1) or 4φ3 and 3φ2 type] are derived for the q-12j coefficients of the first kind (with braiding) instead of the usual expansions in terms of q-6j coefficients. Stretched and doubly stretched q-12j coefficients [as triple, double, or single sums, related to composed or separate hypergeometric 4F3(1) and 5F4(1) or 4φ3 and 5φ4 series and, particularly, to q-9j or q-6j coefficients] are considered.© 2002 American Institute of Physics.
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  • 21
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    Journal of Mathematical Physics 43 (2002), S. 1584-1597 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this work we establish a relationship between Cartan's geometric approach to third-order ordinary differential equations and the three-dimensional null surface formulation. We then generalize both constructions to allow for caustics and singularities that necessarily arise in these formalisms. © 2002 American Institute of Physics.
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  • 22
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    Journal of Mathematical Physics 43 (2002), S. 1569-1583 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: General solutions of the R(circumflex)TT equation with a maximal number of free parameters in the specrtal decomposition of vector SOq(3) R(circumflex) matrices are implemented to construct modified braid equations (MBE). These matrices conserve the given, standard, group relations of the nine elements of T, but are not constrained to satisfy the standard braid equation (BE). Apart from q and a normalization factor our R(circumflex) contains two free parameters, instead of only one such parameter for deformed unitary algebras studied in a previous paper [Math. QA/0009178] where the nonzero right hand side of the MBE had a linear term proportional to (R(circumflex)(12)−R(circumflex)(23)). In the present case the rhs is, in general, nonlinear. Several particular solutions are given (Sec. II) and the general structure is analyzed (Appendix A). Our formulation of the problem in terms of projectors yields also two new solutions of standard (nonmodified) braid equation (Sec. II) which are further discussed (Appendix B). The noncommutative three-spaces obtained by implementing such generalized R(circumflex) matrices are studied (Sec. III). The role of coboundary R(circumflex) matrices (not satisfying the standard BE) is explored. The MBE and Baxterization are presented as complementary facets of the same basic construction, namely, the general solution of R(circumflex)TT equation (Sec. IV). A new solution is presented in this context. As a simple but remarkable particular case a nontrivial solution of BE is obtained (Appendix B) for q=1. This solution has no free parameter and is not obtainable by twisting the identity matrix. In the concluding remarks (Sec. V), among other points, generalization of our results to SOq(N) is discussed. © 2002 American Institute of Physics.
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  • 23
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    Journal of Mathematical Physics 43 (2002), S. 1598-1621 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A recently proposed technique to solve a class of second order functional difference equations arising in electromagnetic diffraction theory is further investigated by applying it to a case of intermediate complexity. The proposed approach is conceptually simple and relies on first obtaining well-defined branched solutions to a pair of associated first order difference equations. The construction of these branched expressions leads to an equation system whose solution requires relationships akin to Riemann's bilinear relations for differentials of the first and third kinds; their derivation necessitates the application of Cauchy's theorem on Riemann surfaces of, in this particular instance, genera one and three. Branch-free solutions of the second order difference equation are then obtained by taking appropriate linear combinations of the branched solutions of the first order equations. Analysis and computation demonstrate that the resulting expressions have the desired analytical properties and recover known solutions in the appropriate limit. © 2002 American Institute of Physics.
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  • 24
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    Journal of Mathematical Physics 43 (2002), S. 904-917 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The generalization à la Kolmogorov of Tsallis entropy, introduced by the authors in a previous work [J. Math. Phys. 37, 4480 (1996)], is revisited. Invariance properties are pointed out under weaker conditions than before. This result leads us to wonder if Tsallis entropy at the Kolmogorov abstraction level brings new information with respect to the generalization that Kolmogorov did of Shannon entropy. The negative answer motivates us to look for other generalizations of Tsallis entropy in order to avoid the lack of new information. Correlation entropies seem to be good candidates for this purpose. The relationship of this kind of entropy with the multifractal analysis is studied with the help of the thermodynamic formalism. We also outline its usefulness to generalize properties of Tsallis entropy. © 2002 American Institute of Physics.
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  • 25
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    Journal of Mathematical Physics 43 (2002), S. 897-903 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that for any central potential V(r) there exist a series of conserved aphelion and perihelion vectors R˜=p×L−g(r)r, g(r)=rV′(r). However, if and only if V(r) is a pure or screened Coulomb potential, R˜ and L constitute an SO4 algebra in the subspace spanned by the degenerate states with a given energy eigenvalue E〈0 at the aphelia and perihelia (r(overdot)=0). For a pure Coulomb potential, R˜ is reduced to the Pauli–Runge–Lenz (PRL) vector R and for a screened Coulomb potential R˜ is reduced to the extended PRL vector R′. While dR/dt=0 always holds, dR′/dt=0 holds only at the aphelia and perihelia. Moreover, the space spanning the SO4 algebra for a screened Coulomb potential is smaller than that for a pure Coulomb potential. The relation of closed orbits for a screened Coulomb potential with that for a pure Coulomb potential is clarified. The ratio of the radial frequency ωr and angular frequency ωφ, ωr/ωφ=κ=1 for a pure Coulomb potential irrespective of the angular momentum L and energy E(〈0). For a screened Coulomb potential κ is determined by the angular momentum L, and when κ is any rational number (κ〈1), the orbit is closed. The situation for a pure or screened isotropic harmonic oscillator is similar. © 2002 American Institute of Physics.
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  • 26
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    Journal of Mathematical Physics 43 (2002), S. 918-953 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We prove that the short distance asymptotics for the even Ising model scaling functions from below Tc is given by the Luther–Peschel formula. Generalizations to the odd scaling functions and holonomic fields are given. © 2002 American Institute of Physics.
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  • 27
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    Journal of Mathematical Physics 43 (2002), S. 954-969 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Several families of classical integrable systems with two degrees of freedom are derived from phase-space realizations of sl(2) Poisson coalgebras. As a remarkable fact, the existence of the N-dimensional integrable generalization of all these systems is always ensured (by construction) due to their underlying dynamical coalgebra symmetry. By following the same approach, different integrable deformations for such systems are obtained from the q-deformed analogues of sl(2). The well-known Jordan-Schwinger realization is also proven to be related to a (non-coassociative) coalgebra structure on sl(2) and the 2 N dimensional integrable Hamiltonian generated by such Jordan-Schwinger representation is obtained. Finally, the relation between complete integrability and the properties of the initial phase-space realization is elucidated through two more examples based on the Heisenberg-Weyl and so(3,2) Poisson coalgebras. © 2002 American Institute of Physics.
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  • 28
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    Journal of Mathematical Physics 43 (2002), S. 984-1007 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The generation of dark solitons due to a small change of the initial data is studied within the framework of the intermediate nonlinear Schrödinger (INLS) equation. In particular, we analyze the spectral problem associated with the INLS equation when the potential consists of a small perturbation imposed on a constant background. We derive a criterion for the perturbation to generate a pair of new discrete eigenvalues as well as their explicit expressions in terms of the perturbation. In addition, we demonstrate that the eigenvalues appear without a threshold on the magnitude of the perturbation. We also consider both the shallow- and deep-water limits of various results obtained for the INLS spectral problem. In the former case, the limiting procedure can be performed smoothly whereas in the latter case, the spectral equation exhibits a new feature of bound states, showing that the eigenvalue is exponentially small compared with the magnitude of the perturbation. © 2002 American Institute of Physics.
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  • 29
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    Journal of Mathematical Physics 43 (2002), S. 970-983 
    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: A Hamiltonian with two degrees of freedom is said to be superintegrable if it admits three functionally independent integrals of the motion. This property has been extensively studied in the case of two-dimensional spaces of constant (possibly zero) curvature when all the independent integrals are either quadratic or linear in the canonical momenta. In this article the first steps are taken to solve the problem of superintegrability of this type on an arbitrary curved manifold in two dimensions. This is done by examining in detail one of the spaces of revolution found by G. Koenigs. We determine that there are essentially three distinct potentials which when added to the free Hamiltonian of this space have this type of superintegrability. Separation of variables for the associated Hamilton–Jacobi and Schrödinger equations is discussed. The classical and quantum quadratic algebras associated with each of these potentials are determined. © 2002 American Institute of Physics.
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  • 30
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    Journal of Mathematical Physics 43 (2002), S. 113-125 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The noncommutative harmonic oscillator, with noncommutativity not only in position space but also in phase space, in arbitrary dimension is examined. It is shown that the (small star, filled)-genvalue problem, which replaces the Schrödinger problem in this case, can be decomposed into separate harmonic oscillator equations for each dimension. The two-dimensional noncommutative harmonic oscillator (four noncommutative phase-space dimensions) is investigated in greater detail. The requirement of the existence of rotationally symmetric solutions leads to a two parameter harmonic oscillator which is completely solved in this case. The angular momentum operator is derived and its (small star, filled)-genvalue problem is shown to be equivalent to the usual eigenvalue problem of the (small star, filled)-genfunction related wave function. The (small star, filled)-genvalues of the angular momentum are found to depend on the energy difference of the oscillations in the two dimensions. Furthermore two examples of a symmetric noncommutative harmonic oscillators are analyzed. The first is the noncommutative two-dimensional Landau problem with harmonic oscillator potential, which shows degeneracy in the energy levels for certain critical values of the noncommutativity parameters, and the second is the three-dimensional harmonic oscillator with noncommuting coordinates and momenta. © 2002 American Institute of Physics.
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  • 31
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    Journal of Mathematical Physics 43 (2002), S. 452-465 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider the existence and the approximation of the global attractor for second-order damped lattice dynamical systems. © 2002 American Institute of Physics.
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  • 32
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    Journal of Mathematical Physics 43 (2002), S. 43-51 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Dirac equation for an electron in two spatial dimensions in the Coulomb and homogeneous magnetic fields is an example of the so-called quasi-exactly solvable models. The solvable parts of its spectrum were previously solved from the recursion relations. In this work we present a purely algebraic solution based on the Bethe ansatz equations. It is realized that, unlike the corresponding problems in the Schrödinger and the Klein–Gordon cases, here the unknown parameters to be solved for in the Bethe ansatz equations include not only the roots of the wave function assumed, but also a parameter from the relevant operator. We also show that the quasi-exactly solvable differential equation does not belong to the classes based on the algebra sl2. © 2002 American Institute of Physics.
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  • 33
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    Journal of Mathematical Physics 43 (2002), S. 466-472 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A direct method for establishing integrable couplings is proposed in this paper. As an example illustration, integrable couplings of TD hierarchy are obtained by constructing a suitable transformation of Lax pairs and a new Lie algebra. © 2002 American Institute of Physics.
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  • 34
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    Journal of Mathematical Physics 43 (2002), S. 473-491 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A prescription for computing the propagator for D-dimensional higher-derivative gravity theories, based on the Barnes–Rivers operators, is presented. A systematic study of the tree-level unitarity of these theories is developed and the agreement of their linearized versions with Newton's law is investigated by computing the corresponding effective nonrelativistic potential. Three-dimensional quadratic gravity with a gravitational Chern–Simons term is also analyzed. A discussion on the issue of light bending within the framework of both D-dimensional quadratic gravity and three-dimensional quadratic gravity with a Chern–Simons term is provided as well. © 2002 American Institute of Physics.
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  • 35
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    Journal of Mathematical Physics 43 (2002), S. 492-507 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the set of invariants CZ [E. Zakhary and J. Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space–times whose Ricci tensors do not possess a null eigenvector. We show that all cases are completely backsolvable in terms of sets of invariants from CZ. We provide algebraically complete sets for each canonically different space–time. © 2002 American Institute of Physics.
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  • 36
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 508-518 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A nonsingular static and spherically symmetric space–time endowed with nonminimally coupled scalar field described by the action S=∫d4 x (−g/2)(R−gαβφ,α φ,β−ξ R φ2) is presented for the case in which the coupling parameter ξ〉1/6. This solitonlike space–time is obtained using the technique of conformal transformation that associates solutions produced by ordinary scalar fields in general relativity with those with nonminimally coupled scalar fields. The dynamical stability of the solution is examined through the Galerkin method. © 2002 American Institute of Physics.
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  • 37
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    Journal of Mathematical Physics 43 (2002), S. 52-55 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the homogeneous properties of metallic 2D photonic crystals. We give a rigorous proof that the limits when the ratio period over wavelength tends to zero and the conductivity tends to infinity do not commute. © 2002 American Institute of Physics.
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  • 38
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    Journal of Mathematical Physics 43 (2002), S. 554-562 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this note we prove a theorem on nonvacuum initial data for general relativity. The result presents a "rigidity phenomenon" for the extrinsic curvature, caused by the nonpositive scalar curvature. More precisely, we claim that in the case of an asymptotically flat nonvacuum initial data if the spatial metric has everywhere nonpositive scalar curvature, then the extrinsic curvature cannot be compactly supported. © 2002 American Institute of Physics.
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  • 39
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    Journal of Mathematical Physics 43 (2002), S. 519-553 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We address the question of the existence and construction of nontrivial, regular solutions of the Einstein–conformally invariant massless scalar field equations, i.e., solutions (g,Φ) satisfying (1−αΦ2)Rμν=α(4∇μΦ∇νΦ−2Φ∇μ∇νΦ−gμν∇σΦ∇σΦ), ∇μ∇μΦ=0, and additionally geometry and the scalar field are regular across the degeneracy region defined as the zeros of (1−αΦ2). Under the assumptions (1) the solution (g,Φ) is minimally of class C3 and admits a hypersurface orthogonal, timelike Killing vector field ξ, and (2) relative to the three spacelike hypersurfaces perpendicular to the Killing field, the degeneracy region constitute regular two-surfaces, and the induced positive definite three metric possesses a degenerate Ricci, we show that the conformal system admits nontrivial, regular across the degeneracy region solutions and we demonstrate that any such solution necessarily admits an additional local G(3) group of isometries possessing two-dimensional orbits of constant Gaussian curvature coinciding with the Φ=cons- equipotential two surfaces. Those solutions exhibit similar properties as the Levi–Civita–Ehlers–Kundt class of static solutions of Einstein's vacuum equations. We investigate this coincidence and in particular we probe the origin of the additional local G(3) group of isometries exhibited by both classes of solutions. From the partial differential equations point of view, both systems, i.e., conformal system as well as the vacuum system, degenerate or become singular, the conformal system along solutions subject to αΦ2=1 within the static region, the vacuum along solutions subject to V=(−ξ⋅ξ)1/2→0+. We demonstrate that as a consequence of the singular nature of the dynamical equations, among all solutions possessing degenerate Ricci in the open vicinity of αΦ2=1, respectively, V→0+, the only regular across degeneracy region solutions are those characterized by a vanishing York–Cotton tensor and, furthermore, such solutions necessarily admit an additional local G(3) group of isometries possessing two-dimensional orbits of constant Gaussian curvature. © 2002 American Institute of Physics.
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  • 40
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    Journal of Mathematical Physics 43 (2002), S. 563-596 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we use a general version of Fermat's principle for light rays in general relativity and a curve shortening method to write the Morse relations for light rays joining an event with a smooth timelike curve in a Lorentzian manifold with boundary. The Morse relations are obtained under the most general assumptions and one can apply them to have a mathematical description of the gravitational lens effect in a very general context. Moreover, Morse relations can be used to check if existing models are corrected.© 2002 American Institute of Physics.
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  • 41
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    Journal of Mathematical Physics 43 (2002), S. 56-68 
    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: We provide geometric quantization of the vertical cotangent bundle V*Q→Q→R, equipped with the canonical Poisson structure and treated as a momentum phase space of nonrelativistic time-dependent mechanics. We show that this quantization is equivalent to fiberwise quantization of symplectic fibers of V*Q→R and that the quantum algebra of time-dependent mechanics is an instantwise algebra. Quantization of the classical evolution equation defines a connection on this instantwise algebra and describes quantum evolution in time-dependent mechanics as a parallel transport. © 2002 American Institute of Physics.
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  • 42
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    Journal of Mathematical Physics 43 (2002), S. 597-603 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Scaling behavior in the moduli space of monopole and dyon solutions in the Einstein–Yang–Mills theory in the asymptotically anti-de Sitter space is derived. The mass of monopoles and dyons scales with respect to their magnetic and electric charges, independent of the values of the cosmological constant and gauge coupling constant. The stable monopole and dyon solutions are approximated by solutions in the fixed anti-de Sitter spacetime. Unstable solutions can be viewed as the Bartnik–McKinnon solutions dressed with monopole and dyon solutions in the fixed anti-de Sitter space. © 2002 American Institute of Physics.
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  • 43
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    Journal of Mathematical Physics 43 (2002), S. 604-620 
    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: Formulas for the expansion of arbitrary invariant group functions in terms of the characters for the Sp(2N), SO(2N+1), and SO(2N) groups are derived using a combinatorial method. The method is similar to one used by Balantekin to expand group functions over the characters of the U(N) group. All three expansions have been checked for all N by using them to calculate the known expansions of the generating function of the homogeneous symmetric functions. An expansion of the exponential of the traces of group elements, appearing in the finite-volume gauge field partition functions, is worked out for the orthogonal and symplectic groups. © 2002 American Institute of Physics.
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  • 44
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    The Journal of Chemical Physics 117 (2002), S. 3897-3914 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The properties of Xe, CH4 and C16H34 lubricant confined between two approaching solids are investigated by a model that accounts for the curvature and elastic properties of the solid surfaces. We consider both smooth surfaces, and surfaces with short-scale roughness. In most cases we observe well defined molecular layers develop in the lubricant film when the width of the film is of the order of a few atomic diameters, but in some cases atomic scale roughness inhibit the formation of these layers, and the lubricant exhibit liquid-like properties. An external squeezing-pressure induces discontinuous, thermally activated changes in the number n of lubricant layers. We observe that the layering transition tends to nucleate in disordered or imperfect regions in the lubrication film. We also present and discuss results of sliding dynamics for Xe and C16H34 lubrication films. © 2002 American Institute of Physics.
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  • 45
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    The Journal of Chemical Physics 117 (2002), S. 3915-3927 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A framework for estimating heating and expected temperature rise in current carrying molecular junctions is described. Our approach is based on applying the Redfield approximation to a tight binding model for the molecular bridge supplemented by coupling to a phonon bath. This model, used previously to study thermal relaxation effects on electron transfer and conduction in molecular junctions, is extended and used to evaluate the fraction of available energy, i.e., of the potential drop, that is released as heat on the molecular bridge. Classical heat conduction theory is then applied to estimate the expected temperature rise. For a reasonable choice of molecular parameters and for junctions carrying currents in the nA range, we find the temperature rise to be a modest few degrees. It is argued, however, that using classical theory to describe heat transport away from the junction may underestimate the heating effect. © 2002 American Institute of Physics.
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  • 46
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    The Journal of Chemical Physics 117 (2002), S. 3886-3896 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We performed molecular dynamics simulations of the diffusion of interstitial He and H2O in ice Ih and found diffusion hops for these interstitial molecules from a stable site to an adjacent site. By observing the jumps of these diffusing species, we determined the jump frequencies, the crystal orientation dependence of the diffusion coefficients, and the diffusion activation energies. Most jumps are along the c axis, because the energy barrier for diffusion along the c axis is lower than that in the a–b plane. Furthermore, the diffusion mechanism for He significantly differ from that for H2O; interstitial H2O diffused by distorting the ice lattice, whereas He atom migrated by jumping from a stable interstitial site to an adjacent site without distorting the lattice. The transverse optic mode for translational lattice vibrations of the lattice surrounding the interstitial H2O shifts to high energy in comparison with that of the pure ice Ih. This upward shift is attributed to a strong coupling between localized translational vibrations of the interstitial H2O and lattice vibrations. The ice lattice is distorted by the translational vibration of the interstitial H2O, since the vibration energy of the mode is close to the energy region of the lattice vibrations of the ice Ih. We conclude that the localized vibrational motion of interstitial molecule is one of the dominant factors governing the diffusion mechanism of the molecule in the ice crystal. © 2002 American Institute of Physics.
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  • 47
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    The Journal of Chemical Physics 117 (2002), S. 3541-3547 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new algorithm for computing anharmonic vibrational states for polyatomic molecules is proposed. The algorithm starts with the vibrational self-consistent field (VSCF) method and uses degenerate perturbation theory to correct for effects of correlation between different vibrational modes. The algorithm is developed in a version that computes the anharmonic vibrational spectroscopy directly from potential energy surface points calculated by using ab initio codes. The method is applied to several molecules where near degeneracies occur for excited vibrational states, including HOOH, HSSH, and HOOOH. The method yields results in very good accordance with experiments and generally provides improvements over nondegenerate perturbation corrections for VSCF. © 2002 American Institute of Physics.
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  • 48
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    The Journal of Chemical Physics 117 (2002), S. 3570-3582 
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    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The long standing problem of the inability of many semiempirical models to correctly predict the polarization of the higher dipole allowed optical transitions of phenyl based π-conjugated polymers and molecules is examined and related to the issue of internal and external screening of π–π electron Coulomb interactions within the molecules. Following a review of previous theoretical and experimental work, π electron only the Complete Neglect of Differential Overlap (CNDO) model is presented which, for the first time, is able to predict accurately the energies and symmetries of all the observed optical transitions of benzene, biphenyl and trans-stilbene, up to ∼8–10 eV. In so doing, it is demonstrated that the problem with previous calculations was the noninclusion of screening from outside the π electron system itself. By fitting separately the spectra in hydrocarbon based condensed phases, in the gas phase and in solid rare gas matrices, and comparing the resulting model parameters, we show that, while the effects of screening from the environment are certainly noticeable, the most important spectral features—in particular the ordering of dipole allowed transitions—come from effective screening by the σ electrons. We find that both of these effects can be adequately accounted for within a π electron only model by using a dielectric constant and appropriate parameter renormalization. © 2002 American Institute of Physics.
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  • 49
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    The Journal of Chemical Physics 117 (2002), S. 3605-3616 
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    Topics: Physics , Chemistry and Pharmacology
    Notes: An approximate functional for the chemical potential of a solute in solution is presented in the energy representation. This functional is constructed by adopting the Percus–Yevick-like approximation in the unfavorable region of the solute–solvent interaction and the hypernetted-chain-like approximation in the favorable region. The chemical potential is then expressed in terms of energy distribution functions in the solution and pure solvent systems of interest, and is given exactly to second order with respect to the solvent density and to the solute–solvent interaction. In the practical implementation, computer simulations of the solution and pure solvent systems are performed to provide the energy distribution functions constituting the approximate functional for the chemical potential. It is demonstrated that the chemical potentials of nonpolar, polar, and ionic solutes in water are evaluated accurately and efficiently from the single functional over a wide range of thermodynamic conditions. © 2002 American Institute of Physics.
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  • 50
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    The Journal of Chemical Physics 117 (2002), S. 3639-3646 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Relativistic core-potential calculations have been carried out on Ω states resulting from the interaction of Xe* (5p56s, 3P, 1P) with ground-state Kr atoms as well as for the system Ar* (3p54s, 3P, 1P) with ground-state Ne, using different basis sets and configuration interaction procedures. The present calculations on ArNe, employing larger sets of Rydberg functions than those of the previous calculations, yield totally repulsive potentials for the excited states of ArNe. Similar calculations on XeKr obtain shallow minima (600–860 cm−1) in the potential energy curves of the excited states at large internuclear distances (6.9–7.8 bohr). Dipole transition moments have been calculated and strong radiative transitions are predicted from excited states to the ground state. The 1(I) state, correlating with the metastable 3P2 state of Xe is found to have a small but nonzero dipole transition moment at short and intermediate nuclear distances leading to a radiative lifetime for the v=0 level of this state of 21.0 μs. © 2002 American Institute of Physics.
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  • 51
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    The Journal of Chemical Physics 117 (2002), S. 3675-3686 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a reexamination of the S1–S0 transition of the (benzene)n cluster that appears only in the dimer ion channel and thus has been assigned to an isomer of the neutral dimer other than the extensively studied T-shaped form. Mass-selective resonantly enhanced two-photon ionization (R2PI) excitation and UV–UV (ultraviolet) hole burning spectra are measured in the 000 and 601 vibronic regions. It is established from the observed spectra monitoring three isotopomer channels, (C6H6)2+, [(C6H6)(C6D6)]+, and (C6D6)2+, that efficient fragmentation following ionization prohibits one to observe the two-color R2PI spectra in the parent ion channels, similar to the case for the benzene tetramer as presented in Paper I [J. Chem. Phys. 117, 3656 (2002)]. Three neutral isotopomers containing at least one C6H6 moiety are identified, and this result argues the reassignment of the band system to the neutral benzene trimer with a cyclic form, where the three benzene sites are equivalent. The spectra of the homo isotopomers [(C6H6)3 and (C6D6)3] in the two vibronic regions exhibit small splittings due to the excitation exchange interactions, and this observation is discussed on the symmetry of the cluster geometry. Energetics pertaining to neutral and ionic benzene clusters are also discussed with previous experimental studies to assess a reason of the efficient fragmentation in the ionic states after R2PI for the trimer and larger clusters but not for the dimer. © 2002 American Institute of Physics.
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  • 52
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    The Journal of Chemical Physics 117 (2002), S. 3780-3788 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this and the accompanying paper [L. Smilowitz et al., J. Chem. Phys. 117, 3789, 2002] we present a theoretical treatment and experimental study, respectively, of the β–δ solid state phase transition in the organic nitramine molecule octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX). The transition is thermodynamically first order with a measured latent heat, occurs via nucleation and growth, and exhibits a thermally activated rate of transformation. We construct a two state kinetic model of the system consisting of equilibrium terms first order in the β or δ mole fraction simulating nucleation, and second order in β and δ simulating growth. The model has four rate constants, the temperature dependence of which is described by eight parameters. We use the transition state formulation of the rate constants and apply a thermodynamic model of the activated state that associates the difference in activated state free energy in forward and reverse directions with the equilibrium transition free energy, and identifies the activated state of the growth process with a metastable melt. By associating components of the activated state free energy with independently measured thermodynamic energies we reduce the degrees of freedom to three, which we fix initially by comparison with previously published kinetic data. We apply the model to both the β–δ and δ–β transformations over a temperature range from 300 to 700 K in order to assess the theoretical validity of the model. The model reproduces the half time of the transition over this entire range, spanning conversion times from 106 to 10−4 s. In the accompanying paper we present an experimental study of the kinetics and mechanism of the phase transition based on second harmonic generation spectroscopy. We use second harmonic generation to verify the nucleation and growth mechanism of the transition and measure the mole fraction change with time over a wide range of temperatures. We use the set of parameters established by theoretical considerations in this paper as an initial parameter set and determine an optimized set by comparison with these data. © 2002 American Institute of Physics.
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  • 53
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    The Journal of Chemical Physics 117 (2002), S. 3804-3810 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An expression for the mutual diffusion coefficient of electrolyte solutions on the Smoluchowski level is proposed and is used in Brownian dynamics simulations. In particular, the divergence of this diffusion coefficient due to the long range of hydrodynamic interactions is solved by introducing explicitly the solvent-fixed frame of reference. The result is used to compute the mutual diffusion coefficient of KCl and LiCl aqueous solutions in the framework of the primitive model at room temperature. Simulations with and without hydrodynamic interactions were performed. Results are in excellent agreement with those obtained by an analytical transport theory which was recently proposed [J.-F. Dufrêche et al., J. Chem. Phys. 116, 2085 (2001)] and which yields reliable estimates for transport coefficients. Moreover, it is shown that electrostatic relaxation effects which cancel exactly in the analytical theory have indeed little influence on the mutual diffusion. © 2002 American Institute of Physics.
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  • 54
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    The Journal of Chemical Physics 117 (2002), S. 3822-3836 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Electron transfer processes in Debye solvents are studied using a spectral analysis method recently proposed. Spectral structure of a nonadiabatic two-state diffusion equation is investigated to reveal various kinetic regimes characterized by a broad range of physical parameters; electronic coupling, energy bias, reorganization energy, and solvent relaxation rate. Within this unified framework, several kinetic behaviors of the electron transfer kinetics, including adiabatic Rabi oscillation, crossover from the nonadiabatic to adiabatic limits, transition from the incoherent to coherent kinetic limits, and dynamic bath effect, are demonstrated and compared with results from previous theoretical models. Dynamics of the electron transfer system is also calculated with the spectral analysis method. It is pointed out that in the large reorganization energy case the nonadiabatic diffusion equation exhibits a nonphysical behavior, yielding a negative eigenvalue. © 2002 American Institute of Physics.
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  • 55
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    The Journal of Chemical Physics 117 (2002), S. 3856-3873 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Molecular dynamics simulation is used to study the relaxation of the polarizability anisotropy in liquid ethanol at temperatures of 298 and 348 K. Ethanol molecules are represented by a four-site semi-flexible model in which the internal degree of freedom, corresponding to the torsional motion around the C–O bond, is taken into consideration. The molecular polarizability is calculated using an interaction-site model, based on the modified dipole-induced dipole model developed by Thole. The collective polarizability induced by intermolecular interactions is included using first-order perturbation theory and calculated considering both center–center and site–site models. Results are analyzed in terms of projected variables that allow the decomposition of the total relaxation into orientational and collision-induced components, both of which are influenced by molecular flexibility. We compare our data with the results of low-frequency depolarized Rayleigh light scattering experiments, examining the possibility of separating different relaxation processes from spectroscopic signals in the time and frequency domains. We find that even though the largest contributor to polarizability anisotropy dynamics is orientational relaxation, collision-induced contributions are important, especially at shorter times. Moreover, we show that torsional motion also plays a significant role in the fast decay of the polarizability anisotropy of the system. Although liquid ethanol is strongly associated and its dipolar relaxation is highly collective, we find orientational pair correlation effects on polarizability relaxation to be negligible. A comparison with simulation data previously obtained for methanol suggests that increasing the alcohol chain length decreases the relative importance of OH dynamics in polarizability relaxation. We further show that, as expected for such a structured liquid composed of strongly asymmetric molecules, polarizability and dipole relaxation processes exhibit marked differences. © 2002 American Institute of Physics.
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  • 56
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    The Journal of Chemical Physics 117 (2002), S. 3874-3877 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The selective separation of ethanol from ethanol–water mixtures by ultrasonic atomization has been reported recently by Sato, Matsuura, and Fujii [J. Chem. Phys. 114, 2382 (2001)]. In that work, experimental data were reported that confirmed the generation of an ethanol-rich droplet mist and attempted to explain the selective separation in terms of parametric decay instability of the capillary wave formed during sonication. In the present work, an alternate mechanism based on the conjunction theory has been postulated for the process of ultrasonic atomization. This mechanism involves the formation of cavitating bubbles in the liquid during sonication and their eventual collapse at the liquid surface into a cloud of microbubbles that moves upwards in a capillary fountain jet. The selective separation of alcohols has been explained as a corollary effect of the physical mechanism resulting in a surface excess of alcohol molecules formed at the surface of the microbubbles. The alcohol molecules vaporize into the microbubbles and release an alcohol-rich mist on their collapse in regions of high accumulation of acoustic energy.
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  • 57
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    The Journal of Chemical Physics 117 (2002), S. 3935-3940 
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    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The interaction between a polymer segment and an oil–water interface is represented by an asymmetric square-well potential where the well-depth on one side reflects water–polymer and the well depth on the other side reflects oil–polymer interactions. The polymer is represented by a Gaussian chain. The polymer's density distribution is calculated along a coordinate perpendicular to the interface. Results are obtained as a function of the well width, the well depth and its asymmetry and, most important, the polymer's length. For a symmetric well, the distribution shows a strong maximum at the interface provided that the polymer is sufficiently long. For an asymmetric well, the polymer is also strongly adsorbed at the interface provided that the polymer is sufficiently long and provided that the larger well-depth does not exceed a critical value that depends on the smaller well-depth. The calculations are in substantial agreement with experimental results that indicate nearly irreversible adsorption of long-chain molecules at an oil–water interface. © 2002 American Institute of Physics.
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  • 58
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    The Journal of Chemical Physics 117 (2002), S. 3878-3885 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The dynamics of a molecule immersed in a superfluid medium are considered. Results are derived using a classical hydrodynamic approach followed by canonical quantization. The classical model, a rigid body immersed in incompressible fluid, permits a thorough analysis; its effective Hamiltonian generalizes the usual rigid-rotor Hamiltonian. In contrast to the free rigid rotor, the immersed body is shown to have chaotic dynamics. Quantization of the classical model leads to new and experimentally verifiable features. It is shown, for instance, that chiral molecules can behave as "quantum propellers:" the rotational-translational coupling induced by the superfluid leads to a nonzero linear momentum in the ground state. Hydrogen peroxide is a strong candidate for experimental detection of this effect. The signature is a characteristic splitting of rotational absorption lines. The 101→110 line in hydrogen peroxide, for example, is predicted to split into three lines separated by as much as 0.01 cm−1, which is about the experimental linewidth. © 2002 American Institute of Physics.
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  • 59
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    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 117 (2002), S. 3941-3950 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We analyze the layering structure for the free liquid surface observed at low temperature in simple fluid models, with pair interaction potentials. The relationship of the surface layers with the Fisher–Widom line is discussed, by direct comparison of Monte Carlo simulation results for the liquid–vapor density profiles and the pair distribution function of the bulk liquid. Also we study the role of the capillary waves in the damping of the surface oscillatory profiles, with Monte Carlo simulations for different transverse areas, and through the theoretical scaling forms using the values of the surface tension given by our simulations. The main conclusion is that the dependence of the surface layering with the temperature is dominated by the capillary waves, even at the small transverse sizes typically used in computer simulations. In contrast, the Fisher–Widom line seems to be of minor importance for the amplitude of the layering. © 2002 American Institute of Physics.
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  • 60
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    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 117 (2002), S. 4030-4041 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Brownian dynamics (BD) simulations of a linear freely jointed bead–rod polymer chain with excluded volume (EV) interaction have been performed under elongational flow with and without the use of fluctuating hydrodynamic interactions (HI). The dependence of the chain size, shape and intrinsic elongational viscosity on the elongational rate cursive-epsilon(overdot) are reported. A sharp coil–stretch transition is observed when cursive-epsilon(overdot) exceeds a critical value, cursive-epsilon(overdot)c. The inclusion of the HI leads to a shift in the coil–stretch transition to higher flow values. Chain deformation due to elongational flow is observed to first consist of the alignment of the chain with the direction of flow without significant chain extension followed by additional alignment of the bond vectors with the flow direction and chain extension as flow rate is increased further. The distribution function for the chain's radius of gyration becomes significantly broader within the transition region which implies an increase in fluctuations in the chain size in this region. The structure factors parallel and perpendicular to the flow direction illustrate different elongational rate dependencies. At high rates, the structure factor in the direction of the flow exhibits an oscillating dependence which corresponds to the theoretically predicted shape for a rigid-rod model. The mean squared orientation of each bond within the chain with respect to the flow direction as function of bond number is nearly parabolic in shape with the highest degree of orientation found within the chain's interior. The dependence of the critical elongational rate, cursive-epsilon(overdot)c, on the chain length, N, is observed to be cursive-epsilon(overdot)c∼N−1.96 when hydrodynamic interactions are not employed and cursive-epsilon(overdot)c∼N−1.55 when they are invoked. These scaling exponents agree well with those obtained in previous BD simulations of bead-FENE (i.e., finitely extensible nonlinear elastic) spring chains as well as with the theoretical predictions of cursive-epsilon(overdot)c∼N−2 and cursive-epsilon(overdot)c∼N−1.5 without and with hydrodynamic interactions based on the Rouse and Zimm models, respectively. © 2002 American Institute of Physics.
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  • 61
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    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 117 (2002), S. 2995-3002 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Second-order quantized Hamiltonian dynamics (QHD-2) is mapped onto classical mechanics by doubling the dimensionality. The mapping establishes the classical canonical structure for QHD-2 and permits its application to problems showing zero-point energy and tunneling via a standard molecular dynamics simulation, without modifying the simulation algorithms, by introducing new potentials for the extra variables. The mapping is applied to the family of Gaussian approximations, including frozen and thawed Gaussians, which are special cases of QHD-2. The mapping simplifies numerous applications of Gaussians to simulations of spectral intensities and line shapes, nonadiabatic and other quantum phenomena. The analysis shows that frozen Gaussians conserve the total energy, while thawed Gaussians do not, unless an additional term is introduced to the equation of motion for the thawed Gaussian momentum. The classical mapping of QHD-2 is illustrated by tunneling and zero-point energy effects in the harmonic oscillator, cubic and double-well potential, and the Morse oscillator representing the O–H stretch of the SPC-F water model. © 2002 American Institute of Physics.
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  • 62
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    The Journal of Chemical Physics 117 (2002), S. 3027-3039 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper we present a new approach to simulation methods for classical statistical mechanics relying on a field-theoretical formalism. It is based on applying the complex Hubbard–Stratonovich transformation to the canonical and grand-canonical partition function, which allows one to reexpress their particle representation in terms of a functional integral over a fluctuating auxiliary field. The thermodynamic averages from the resulting field representations can then be calculated with a conventional Monte Carlo algorithm. We explored the applicability of the auxiliary field methodology for both the canonical and grand-canonical ensemble using a system of particles interacting through a purely repulsive Gaussian pair potential in a broad range of external parameters. In the grand-canonical case this technique represents an alternative to standard grand-canonical Monte Carlo methods. Generally providing a framework for simulating classical particle systems within a continuum formalism can be useful for multiscale modeling where the field or continuum description naturally appears within quantum mechanics on smaller length scales and within classical mechanics on larger ones.© 2002 American Institute of Physics.
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  • 63
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    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 117 (2002), S. 3003-3012 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We present a method for computing intermolecular energies of large molecules based on a suitable fragmentation scheme, which allows one to express the complete interaction energy as a sum of interaction energies between pairs of fragments. The main advantage consists in the possibility of using standard ab initio quantum methods to evaluate the fragment energies. For the 4-n-pentyl-4′-cyanobiphenyl (5CB) dimer, the present results indicate that the most favorite arrangement corresponds to an antiparallel side-by-side geometry with a stabilization energy of about 16 kcal/mol. It is shown that, by the present method, the interaction energy of the 5CB dimer can be evaluated for all geometrical conformations and, in principle, it can be used for bulk simulations. © 2002 American Institute of Physics.
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  • 64
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    The Journal of Chemical Physics 117 (2002), S. 3081-3087 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this work, we present a generalized version of the semirigid vibrating rotor target (SVRT) model by including additional vibrational modes explicitly in the SVRT Hamiltonian. The inclusion of additional vibrational modes eliminates the uncertainty of fixing certain geometries of the target molecule as required in the basic SVRT model. This generalized SVRT (GSVRT) model was employed to study the benchmark reaction H+CH4 by including the umbrella mode of CH4. Influence of the umbrella mode of the reagent on reactivity is investigated. It is concluded that the inclusion of the umbrella vibrational mode of CH4 has only a small effect on the reaction from the ground state of the reagent, and essentially no effect from the excited C–H stretching vibrational state of the reagent. However, the initial excitation of the umbrella mode does give a sizable enhancement of reaction and reduces the reaction barrier by about 1.1 kcal/mol. © 2002 American Institute of Physics.
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  • 65
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    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 117 (2002), S. 3109-3119 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The near-dissociation microwave rovibronic spectra of HeN+ [Carrington et al., Chem. Phys. Lett. 262, 598 (1996)] are used to obtain coupled potential energy curves for the six electronic states correlating with He+N+ 3P0, 3P1, and 3P2. High-quality ab initio calculations are carried out, using a spin-restricted open-shell coupled-cluster method with an augmented correlation-consistent quintuple-zeta basis set (aug-cc-pV5Z). Fully coupled calculations of bound and quasibound states are performed, including all six electronic states, and suggest two possible assignments of the observed transitions. The potentials are then morphed (scaled) to reproduce the experimental frequencies. One of the two assignments, designated SH1, is preferred because it gives a more satisfactory explanation of the observed hyperfine splittings. The corresponding morphed potential has well depths of 1954 cm−1 and 192 cm−1 for the spin-free 3Σ− and 3Π curves, respectively. © 2002 American Institute of Physics.
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  • 66
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    The Journal of Chemical Physics 117 (2002), S. 2990-2990 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: © 2002 American Institute of Physics.
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  • 67
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    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 117 (2002), S. 1941-1955 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The so-called energy-corrected coupled-cluster method with singles and doubles (CCSD), which is closely related to the recently proposed method of moments of Kowalski and Piecuch, accounts for the nondynamic correlation effects, which are missing in the standard single-reference CCSD, by projecting onto the modest-size multireference (MR) configuration-interaction SD (CISD) wave function when evaluating the energy, rather than onto the single-determinantal CCSD reference. The ability of this approach to generate reliable potential energy curves (PECs) or surfaces over a wide range of geometries is examined using a realistic ab initio model of the HF molecule. The PECs obtained with the correlation-consistent polarized valence double (triple, quadruple) zeta cc-pVXZ (T,Q) basis sets are used, together with the PEC extrapolated to the complete basis set limit, to compute the rotational and vibrational levels, which are then compared with the experimentally determined values as well as with the directly measured vibrational frequencies. A comparison is also made with the earlier results [X. Li, J. Mol. Struct.: THEOCHEM 547, 69 (2001)] that were obtained with the amplitude-corrected CCSD method, namely the so-called reduced MR CCSD that exploits the same MR CISD wave function, as well as with recently published renormalized CCSD(T) results [P. Piecuch et al., J. Chem. Phys. 115, 5796 (2001)]. It is shown that both the amplitude- and energy-corrected CCSD PECs may be used to generate highly accurate and reliable spectroscopic data once the basis set limit is achieved. © 2002 American Institute of Physics.
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  • 68
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    The Journal of Chemical Physics 117 (2002), S. 1975-1981 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Charged systems interacting via Coulomb forces can be efficiently simulated by introducing a local, diffusing degree of freedom for the electric field. This paper formulates the continuum electrodynamic equations corresponding to the algorithm and studies the spectrum of fluctuations when these equations are coupled to mobile charges. I compare the calculations with simulations of a charged lattice gas, and study the dynamics of charge and density fluctuations. The algorithm can be understood as a realization of a mechanical model of the ether. © 2002 American Institute of Physics.
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  • 69
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    The Journal of Chemical Physics 117 (2002), S. 2017-2029 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The reaction dynamics of ground-state atomic oxygen [O(3P)] with allyl radicals (C3H5) has been investigated by applying a combination of crossed beams and laser induced fluorescence techniques. The reactants O(3P) and C3H5 were produced by the photodissociation of NO2 and the supersonic flash pyrolysis of precursor allyl iodide, respectively. A new exothermic channel of O(3P)+C3H5→C3H4+OH was observed and the nascent internal state distributions of the product OH (X 2Π:υ″=0,1) showed substantial bimodal internal excitations of the low- and high-N″ components without Λ-doublet and spin–orbit propensities in the ground and first excited vibrational states. With the aid of the CBS-QB3 level of ab initio theory and Rice–Ramsperger–Kassel–Marcus calculations, it is predicted that on the lowest doublet potential energy surface the major reaction channel of O(3P) with C3H5 is the formation of acrolein (CH2CHCHO)+H, which is consistent with the previous bulk kinetic experiments performed by Gutman et al. [J. Phys. Chem. 94, 3652 (1990)]. The counterpart C3H4 of the probed OH product in the title reaction is calculated to be allene after taking into account the factors of reaction enthalpy, barrier height and the number of intermediates involved along the reaction pathway. On the basis of population analyses and comparison with prior calculations, the statistical picture is not suitable to describe the reactive atom-radical scattering processes, and the dynamics of the title reaction is believed to proceed through two competing dynamical pathways. The major low N″-components with significant vibrational excitation may be described by the direct abstraction process, while the minor but extraordinarily hot rotational distribution of high N″-components implies that some fraction of reactants is sampled to proceed through the indirect short-lived addition-complex forming process. © 2002 American Institute of Physics.
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  • 70
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    The Journal of Chemical Physics 117 (2002), S. 3278-3288 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We analyze the correlated motions of hydrogen bonded clusters in liquid hydrogen fluoride, methanol, and water using the Instantaneous Normal Mode approach. In the case of hydrogen fluoride and methanol, which form a topologically linear hydrogen bond network, the relevant cluster is a triplet formed by a molecule and its two neighbors. In the case of water, whose hydrogen bond structure has a local tetrahedral symmetry, the basic unit considered is the pentamer formed by a molecule and its four neighbors. For each of these clusters we identify, using symmetry arguments, the a priori modes describing the relative motions of the cluster molecules and introduce suitable projections in order to evaluate how much these modes contribute to the actual motions at different frequencies. In the case of hydrogen fluoride we confirm the assignment of a 50 rad/ps peak observed in the single and collective correlation function spectra to the stretching of the hydrogen bonded network. In the case of methanol the analysis of the correlated motions of the triplets shows that in the intermediate frequency range (around 25 rad/ps) a picture similar to what is observed in hydrogen fluoride applies, whereas the high frequency properties of the liquid (beyond 50 rad/ps) are mostly due to the asymmetric stretching motion. In the case of water we demonstrate that the a priori modes, based on the full tetrahedral symmetry of the water pentamer, do indeed mix strongly under the effect of the interaction with the neighbors. The results are related to the spectroscopic measurement. © 2002 American Institute of Physics.
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  • 71
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    The Journal of Chemical Physics 117 (2002), S. 3316-3320 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We have studied the medium effects on the frequency-dependent polarizability of water by separating the total polarizability of water clusters into polarizabilities of the individual water molecules. A classical frequency-dependent dipole–dipole interaction model based on classical electrostatics and an Unsöld dispersion formula has been used. It is shown that the model reproduces the polarizabilities of small water clusters calculated with time-dependent density functional theory. A comparison between supermolecular calculations and the localized interaction model illustrate the problems arising from using supermolecular calculations to predict the medium perturbations on the solute polarizability. It is also noted that the solute polarizability is more dependent on the local geometry of the cluster than on the size of the cluster. © 2002 American Institute of Physics.
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  • 72
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    The Journal of Chemical Physics 117 (2002), S. 3345-3353 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We use 42 different charged nanoparticles generated by electrospray ionization and a differential mobility analyzer of unusual resolving power, as well as a condensation chamber of the turbulent-mixing type to study the dependence between the diameter, charge state, and critical supersaturation of embryos promoting heterogeneous nucleation. The nanoparticles investigated have diameters ranging from 0.43 to 6.51 nm, and positive charge states varying between 1 and 5 elementary units. We find that the critical supersaturation of small singly charged ions (mobility diameters bellow 1.01 nm) is independent of their size and its value coincides with the result anticipated by Thompson in his theory of ion-induced nucleation. On the other hand, the supersaturation required to activate multiply charged embryos is consistently higher than Thomson's prediction. In fact, the reduction of the critical supersaturation induced by electrification is much smaller than expected for large and multiply charged embryos, and their critical radius is estimated better by Kelvin's criterion. We speculate that this discrepancy is due to the geometrical differences between the actual nucleation sites and the idealized embryo considered in Thomson's model. © 2002 American Institute of Physics.
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  • 73
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    The Journal of Chemical Physics 117 (2002), S. 3369-3382 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The paper discusses the structure and phase behavior of films adsorbed on the (100) plane of model face-centered cubic crystals characterized by different strength of the surface potential studied by means of Monte Carlo simulation. Melting and disordering of incommensurate and commensurate monolayer and bilayer films formed on strongly attractive surfaces as well as the behavior of small dro