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  • 1
    ISSN: 1572-9613
    Keywords: Equilibrium State ; Correlation Inequalities ; Symmetry Breaking ; Ising Systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new characterization of equilibrium states for classical lattice systems is given in terms of correlation inequalities. Their physical meaning is found to express thermodynamic stability. We demonstrate the applicability of the inequalities in specific models.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1572-9613
    Keywords: Electron-phonon system ; quantum fluctuations ; Peierls instability ; Kohn anomaly
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A mathematical basis is given to the Peierls-Fröhlich instability and the Kohn anomaly. The techniques and ideas are based on the recently developed mathematical theory of quantum fluctuations and response theory. We prove that there exists a unique resonant one-mode interaction between electrons and phonons which is responsible for the Peierls-Fröhlich instability and the phase transition in the Mattis-Langer model. We prove also that the softening of this phonon mode at the critical temperature (Kohn anomaly) is a consequence of the critical slowing down of the dynamics of the lattice distortion fluctuations. It is the result of the linear dependence of two fluctuation operators corresponding to the frozen charge density wave and the distortion order parameter.
    Type of Medium: Electronic Resource
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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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