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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract A gas of two Boson systems coexisting inR 3, and interacting only mutually, is analyzed. The interaction is quadratic, so that the dynamical problem may be solved completely and exactly. The initial state is taken to be the mutually uncorrelated Gibbs states:Φ β (1) ⊗Φ β (2) =Φ ψβ. We find the time evolved state, and its projections onto the separate species and the subvolumes. The principle consequences of this model are discussed. In particular we examine the possible occurrence of harmonic oscillations between the species.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 1063-1073 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Among the multiplication operators on weighted Bergman Hilbert spaces are those where the multiplying function (operator symbol) depends only on the angular polar coordinate in the unit disk: we call these "angle operators." As these Hilbert spaces carry a CCR representation unitarily equivalent to the Schrödinger representation, angle operators are associated with quantum phase in the same way as are Toeplitz operators, for example. We determine the matrix elements of the angle operators with respect to the natural orthonormal basis on each of these spaces, and also with respect to the appropriate family of coherent states. By using a method of comparison with the corresponding results for Toeplitz operators, asymptotic expressions for the expectations and variances in these two families of states are obtained for the angle operators whose symbols are the polar angle function and its two complex exponentials. Notable is the fact that the asymptotic limit of the variance of the polar angle operator in the natural basis family is π2/3, which many authors take to be a requirement for a quantum phase operator. © 2002 American Institute of Physics.
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  • 3
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We discuss briefly the basic (integrable)representation of the ucr, comprising the operators A ,its adjoint A+, and N (which is equal toN+), satisfying AN – NA = A. There areno additional relations between the operators, in general. The ucrinclude the ccr, car, deformed bosons and fermions, andmany other systems as special cases. The principalstructure theorem asserts that every integrablerepresentation of the ucr is determined by a sequencegeneralizing the [n]-sequence of deformationtheory.
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 3238-3262 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider *-representations of the unital complex *-algebra generated by the identity and two elements, α and ν, with ν=ν* and one relation, αν−να=α, the ultra-commutation relations (ucr). In general, we do not impose any commutation relation between α and α*. This is a very general scheme, encompassing many important physical examples, inter alia: the ccr, car, q-deformed bosons and fermions. The representations of interest in physics have a diagonal number operator π(ν) whose spectrum is contained in the positive integers (together with some other technical conditions). Our principal result is that every *-representation in this class is completely determined, up to unitary equivalence, by the sequence of numbers [n+1]=|〈Ωn+1,π(α+)Ωn〉|2 for n≥0, with [0]=0. Here Ωn is the normalized eigenvector of π(ν) corresponding to the eigenvalue n if the dimension of that eigenspace is 1. If the carrier Hilbert space is infinite dimensional, this representation is irreducible if and only if [n]〉0 for n≥1. Finally, we consider spatial representations of some of these representations by kernels and differential operators. © 1997 American Institute of Physics.
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 295-324 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: When a single-species plasma is confined in a harmonic Penning trap at cryogenic temperature, the thermal equilibrium is approximately a uniform density spheroid (ellipsoid of revolution). Normal modes corresponding to quadrupole excitations of this plasma have recently been measured. In this paper, nonlinear equations of motion are derived for these quadrupole oscillations. For large amplitudes, the oscillations deform a spheroidal plasma into a triaxial ellipsoid with time-dependent shape and orientation. The integrals of the motion are found and the cylindrically symmetric finite-amplitude oscillations of a spheroid are studied. An analysis of all possible ellipsoidal equilibria is also carried out. New equilibria are discovered which correspond to finite-amplitude versions of the noncylindrically symmetric linear quadrupole oscillations. The equilibria are shown to fall into two classes in which the ellipsoids are either tilted or aligned with respect to the magnetic field. Some of these equilibria have densities well above the Brillouin limit.
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 4 (1992), S. 274-277 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The regime of validity of nonlinear gyrokinetic equations is extended to cover uniformly both the usual drift-kinetic and gyrokinetic regimes through the use of an expansion in the parameter ε∼(ρ/λ⊥)e(φ−v(parallel) Az/c)/T. Here, ρ is the gyroradius, λ⊥ is the scale length of the electrostatic and parallel magnetic potentials φ and Az, c is the speed of light, and T is the temperature. This is made possible by a preparatory split of the potentials into gyrophase-dependent and independent parts. For nonlinear fluctuations saturated at mixing-length levels (e.g., with eφ/T∼λ⊥ /L, where L is the equilibrium scale length), ε is of order ρ/L for all scales λ⊥ ranging from ρ to L, and is therefore small in plasmas of fusion interest.
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  • 8
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 12 (2000), S. 2397-2412 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The inviscid damping of an asymmetric perturbation on a two-dimensional circular vortex is examined theoretically, and with an electron plasma experiment. In the experiment, an elliptical perturbation is created by an external impulse. After the impulse, the ellipticity (quadrupole moment) of the vortex exhibits an early stage of exponential decay. The measured decay rate is in good agreement with theory, in which the perturbation is governed by the linearized Euler equations. Often, the exponential decay of ellipticity is slow compared to a vortex rotation period, due to the excitation of a quasimode. A quasimode is a vorticity perturbation that behaves like a single azimuthally propagating wave, which is weakly damped by a resonant interaction with corotating fluid. Analytically, the quasimode appears as a wave packet of undamped continuum modes, with a sharply peaked frequency spectrum, and it decays through interference as the modes disperse. When the exponential decay rate of ellipticity is comparable to the vortex rotation frequency, the vorticity perturbation does not resemble a quasimode; rather, it is rapidly dominated by spiral filaments. Over longer times, linear theory predicts algebraic decay of ellipticity; however, nonlinear oscillations of ellipticity emerge in the experiment before a transition to algebraic decay would occur. © 2000 American Institute of Physics.
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  • 9
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 11 (1999), S. 905-914 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Vortex-in-cell simulations that numerically integrate the 2D Euler equations are compared directly to experiments on magnetized electron columns [K. S. Fine, A. C. Cass, W. G. Flynn, and C. F. Driscoll, "Relaxation of 2D turbulence to vortex crystals," Phys. Rev. Lett. 75, 3277 (1995)], where turbulent flows relax to metastable vortex crystals. A vortex crystal is a lattice of intense small diameter vortices that rotates rigidly in a lower vorticity background. The simulations and experiments relax at the same rates to vortex crystals with similar vorticity distributions. The relaxation is caused by mixing of the background by the intense vortices: the relaxation rate is peaked when the background circulation is 0.2–0.4 times the total circulation. Close quantitative agreement between experiment and simulation provides strong evidence that vortex crystals can be explained without incorporating physics beyond 2D Euler theory, despite small differences between a magnetized electron column and an ideal 2D fluid. © 1999 American Institute of Physics.
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 7641-7647 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Transition inverse temperatures (or Γ values) at the fluid–solid phase boundary of Yukawa systems near the one-component-plasma (OCP) limit have been evaluated by molecular dynamics simulations. These values are systematically smaller than those obtained in an earlier study by Farouki and Hamaguchi [J. Chem. Phys. 101, 9885 (1994)]. The discrepancy is attributed to the fact that, in the earlier study, the harmonic entropy constants were approximated by that of the OCP, whereas the new results are based on more accurate harmonic entropy constants obtained from lattice-dynamics calculations. The new molecular dynamics simulations also confirm that the bcc–fcc phase transition curve is in good agreement with that of the quasiharmonic theory in the regime κ≤1.4, where κ is the ratio of the Wigner–Seitz radius to the Debye length. Examples of Yukawa systems include dusty plasmas and colloidal suspensions. © 1996 American Institute of Physics.
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