The Thermodynamic Limit of Quantum Coulomb Systems. Part I. General Theory

Hainzl, Christian; Lewin, Mathieu; Solovej, Jan Philip

The Thermodynamic Limit of Quantum Coulomb Systems. Part I. General Theory

Authors

Hainzl, Christian

Lewin, Mathieu

Solovej, Jan Philip

Description

This article is the first in a series dealing with the thermodynamic properties of quantum Coulomb systems. In this first part, we consider a general real-valued function $E$ defined on all bounded open sets of $\R^3$. Our aim is to give sufficient conditions such that $E$ has a thermodynamic limit. This means that the limit $E(Ω_n)|Ω_n|^{-1}$ exists for all `regular enough' sequence $Ω_n$ with growing volume, $|Ω_n|\to\ii$, and is independent of the considered sequence. The sufficient conditions presented in our work all have a clear physical interpretation. In the next paper, we show that the free energies of many different quantum Coulomb systems satisfy these assumptions, hence have a thermodynamic limit.
Final version to appear in Advances in Mathematics