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  • 1
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We consider the finite-volume quantum n-vector anharmonic crystal in the large n limit and compute corrections to the corresponding Hartree–Fock system. In particular we prove the complete 1/n-asymptotic series of the free energy, the Gibbs canonical state, and the distributions of the displacement and squared displacement fluctuation operators.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Communications in mathematical physics 174 (1996), S. 635-660 
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The scaling behaviour of fluctuations of the Bose field Φ(f) in the ergodic infinite volume equilibrium states of ad-dimensional Bose gas at temperatureT and density $$\bar \rho$$ , can be classified in terms of the testfunctionsf. In the low density regime, the space of testfunctions splits up in two subspaces, leading to two different types of non-commuting macroscopic field fluctuation observables. Testfunctionsf with Fourier transform yield normal fluctuation observables. The local fluctuations of the field operators Φ(f) must be scaled subnormally (i.e. with a negative scaling index) if the testfunctionf has $$\hat f(0) = 0$$ . The macroscopic fluctuations of these fields can then again be described by a Bose field. The situation changes when the density of the gas exceeds the critical density. The field operators which have normal fluctuations in the low density regime need to be scaled abnormally in the high density regime, yielding classical macroscopic fluctuation observables. Another difference with the low density regime is that the space of testfunctions with $$\hat f(0) = 0$$ splits up in two subspaces when the critical density is reached: for a first subspace the algebraic character of the macroscopic field fluctuation observables in also classical because it is necessary to scale the fluctuations of the field operators normally, while for the remaining subclass, the same negative scaling index is required as in the low density regime and hence also the algebraic character of these macroscopic fluctuations is again CCR.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 96 (1999), S. 1125-1161 
    ISSN: 1572-9613
    Keywords: spontaneous symmetry breaking ; Goldstone theorem ; normal coordinates ; interacting Bose gases ; Bose–Einstein condensation ; quantum fluctuations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Spontaneous symmetry breaking (SSB) is one of the basic aspects of collective phenomena such as phase transitions in statistical mechanics or ground-state excitations in field theory. In general, spectral analysis of SSB is related to the presence of a Goldstone boson particle. The explicit construction of the canonical variables (boson field operator and its adjoint) of this boson has so far been an open problem. In this paper, we consider the SSB of Bose–Einstein condensation in two models: the so-called imperfect or mean field Bose gas (which is nothing but a perfect ideal Bose gas including the property of equivalence of ensembles), and the Bogoliubov weakly interacting Bose gas. For both we construct explicitly the Goldstone boson field variables. The remarkable result is that in both cases the field and its adjoint field are formed as the “fluctuation operators” respectively of the order parameter operator and of the generator of the broken symmetry. The notion of “fluctuation operator” is essential for our mathematical construction. We find that although the order parameter has a critical fluctuation, the generator of the broken symmetry has a squeezed fluctuation of the same inverse rate. Furthermore, we prove that this canonical pair of variables decouples from the other variables of the system, and that these fluctuations behave dynamically as long-wavelength sound waves or as oscillator variables.
    Type of Medium: Electronic Resource
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  • 4
    ISSN: 1572-9613
    Keywords: Quantum fluctuation operators ; order parameter ; dynamics ; critical line ; phonon spectrum ; soft modes ; central peak problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For a model given previously by the authors describing a structural phase transition we compute theq-mode critical fluctuations of momentum and displacement as a function of the critical temperatures, the wave vectorq, and a fading-out external field. An explicit dependence on the rates of fading out is obtained. In order to define the critical fluctuation operators we prove a reconstruction theorem, which is of model-independent value. Finally we study the critical spectrum and get rigorous results on the soft modes and the central peak.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 6746-6757 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For quantum lattice systems, it is proven that anomalously scaled fluctuations have a natural Lie algebra structure. The harmonic lattice in the ground state is given as an illustration of the general theorem. © 1995 American Institute of Physics.
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1268-1279 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The imperfect Boson gas supplemented with a gentle repulsive interaction is completely solved. In particular, it is proved that it has nonextensive Bose–Einstein condensation, i.e., there is condensation without macroscopic occupation of the ground (k=0) state level. © 1999 American Institute of Physics.
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