Electron gases in toroidal shells: mode coupling and state functions

TL;DR

This paper investigates the quantum states of free electron gases in toroidal shells, revealing mode couplings and calculating thermodynamic properties, which differ from those in solid toroidal volumes.

Contribution

It introduces a basis set expansion tailored to the toroidal geometry to analyze eigenvalues, wave functions, and thermodynamic functions of electron gases in shells.

Findings

Mode couplings are significant at low azimuthal quantum numbers.

Single particle density distributions are modified by mode interactions.

Thermodynamic functions differ from those of solid toroidal volumes.

Abstract

Eigenvalues and wave functions describing free electron gases in toroidal shells are determined using a basis set expansion natural to the system geometry. Couplings between azimuthal and poloidal modes are found to be appreciable at lower values of ${m_\phi}$, modifying single particle density distributions within the shells. Thermodynamic state functions are calculated and contrasted with those of a solid toroidal volume.