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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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