Geometry effects in confined space

TL;DR

This paper derives exact solutions for grand partition functions of quantum gases in various confined geometries, analyzing how finite size and shape influence their thermodynamic properties beyond the thermodynamic limit.

Contribution

It provides explicit solutions for quantum gases in complex geometries and evaluates the validity of quantum statistical methods for confined systems.

Findings

Exact solutions for quantum gases in various confined geometries.

Analysis of geometry effects beyond the thermodynamic limit.

Discussion of geometry effects in realistic systems.

Abstract

In this paper we calculate some exact solutions of the grand partition functions for quantum gases in confined space, such as ideal gases in two- and three-dimensional boxes, in tubes, in annular containers, on the lateral surface of cylinders, and photon gases in three-dimensional boxes. Based on these exact solutions, which, of course, contain the complete information about the system, we discuss the geometry effect which is neglected in the calculation with the thermodynamic limit $V\to \infty $, and analyze the validity of the quantum statistical method which can be used to calculate the geometry effect on ideal quantum gases confined in two-dimensional irregular containers. We also calculate the grand partition function for phonon gases in confined space. Finally, we discuss the geometry effects in realistic systems.