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Semiclassical results in the linear response theory. (English) Zbl 1079.82007

Summary: We consider a quantum system of non-interacting fermions at temperature \(T\), in the framework of linear response theory. We show that semiclassical theory is an appropriate framework to describe some of their thermodynamic properties, in particular through asymptotic expansions in \(\hbar\) (Planck constant) of the dynamical susceptibilities. We show how the closed orbits of the classical motion in phase space manifest themselves in these expansions, in the regime where \(T\) is of the order of \(\hbar\).

MSC:

82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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