Diamagnetic expansions for perfect quantum gases

TL;DR

This paper analyzes the diamagnetic behavior of perfect quantum gases under a constant magnetic field, establishing the existence of thermodynamic limits for pressure and susceptibilities through Taylor series expansions.

Contribution

It introduces a rigorous method to prove the thermodynamic limit for pressure and susceptibilities using Taylor expansions of the Gibbs semigroup.

Findings

Thermodynamic limit exists for pressure.

Thermodynamic limit exists for all derivatives of pressure.

Taylor series expansion in magnetic field parameter converges in various topologies.

Abstract

In this work we study the diamagnetic properties of a perfect quantum gas in the presence of a constant magnetic field of intensity $B$. We investigate the Gibbs semigroup associated to the one particle operator at finite volume, and study its Taylor series with respect to the field parameter $\omega:= eB/c$ in different topologies. This allows us to prove the existence of the thermodynamic limit for the pressure and for all its derivatives with respect to $\omega$ (the so-called generalized susceptibilities).