Semiclassical results in the linear response theory

TL;DR

This paper demonstrates that semiclassical theory effectively describes thermodynamic properties of non-interacting fermions in linear response, highlighting the role of classical closed orbits in asymptotic expansions of susceptibilities when temperature is comparable to Planck's constant.

Contribution

It establishes a connection between semiclassical expansions and classical phase space dynamics for fermionic systems at specific temperature regimes.

Findings

Semiclassical expansions reveal classical closed orbits influence quantum susceptibilities.

Asymptotic expansions are valid when temperature is on the order of Planck's constant.

The approach bridges classical and quantum descriptions in linear response theory.

Abstract

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 $\hbar$.