The Independence on Boundary Conditions for the Thermodynamic Limit of Charged Systems

TL;DR

This paper proves that the thermodynamic limit for charged systems with electrons and nuclei is independent of boundary conditions, extending known results from Dirichlet to other boundary types like Neumann and periodic.

Contribution

It demonstrates that the thermodynamic limit remains consistent across various boundary conditions for scaled domains with smooth boundaries.

Findings

Thermodynamic limit exists for all considered boundary conditions.

Limit is independent of boundary condition type.

Applicable to domains with smooth boundaries and isolated edges or corners.

Abstract

We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such as Neumann, periodic, or elastic boundary conditions. The result is proven for all limiting sequences of domains which are obtained by scaling a bounded open set, with smooth boundary, except for isolated edges and corners.