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

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

2008-06-10

arxiv.org/abs/0806.1708v2

Physics

Mathematical Physics

Final version to appear in Advances in Mathematics

Scientific paper

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 $E(\Omega_n)|\Omega_n|^{-1}$ exists for all `regular enough' sequence $\Omega_n$ with growing volume, $|\Omega_n|\to\ii$, 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.

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