Semiclassical theory for many-body Fermionic systems

TL;DR

This paper develops a semiclassical framework for many-body Fermionic systems, expressing response functions as series expansions involving classical correlations, Weyl-Wigner series, and periodic-orbit corrections, applicable without assuming classical integrability.

Contribution

It introduces a novel semiclassical approach for many-body Fermionic systems that does not require classical integrability, connecting linear response theory with semiclassical expansions.

Findings

Response functions expressed as series with classical and quantum corrections

Framework applicable to non-integrable classical dynamics

Discussion of potential applications in many-body physics

Abstract

We present a treatment of many-body Fermionic systems that facilitates an expression of the well-known quantities in a series expansion of the Planck's constant. The ensuing semiclassical result contains to a leading order of the response function the classical time correlation function of the observable followed by the Weyl-Wigner series, on top of these terms are the periodic-orbit correction terms. The treatment given here starts from linear response assumption of the many-body theory and in its connection with semiclassical theory, it makes no assumption of the integrability of classical dynamics underlying the one-body quantal system. Applications of the framework are also discussed.