量子库仑系统的热力学极限。第一部分.一般理论
The Thermodynamic Limit of Quantum Coulomb Systems. Part I. General Theory
摘要：
本文是讨论量子库仑系统热力学性质系列文章的第一篇。在第一部分中，我们考虑定义在$\R^3$的所有有界开集上的一般实值函数$E$。我们的目的是给出充分条件，使$E$有一个热力学极限。这意味着极限$E(Ω_n)|Ω_n|^{-1}$存在于所有“足够规则”的序列$Ω_n$和增长的体积，$|Ω_n|\to\ii$，并且与所考虑的序列无关。本文提出的充分条件都有明确的物理解释。在接下来的文章中，我们证明了许多不同量子库仑系统的自由能满足这些假设，因此有一个热力学极限。
英文摘要：
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.
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