On the Magnetization of a Charged Bose Gas in the Canonical Ensemble

TL;DR

This paper proves the existence of the thermodynamic limit for the canonical magnetization of a charged Bose gas in a magnetic field and shows its equivalence to the grand canonical magnetization up to surface corrections.

Contribution

It establishes the thermodynamic limit for the canonical magnetization of a charged Bose gas and compares it with the grand canonical magnetization, including surface correction analysis.

Findings

Thermodynamic limit exists for all positive density, temperature, and magnetic field.

Canonical and grand canonical magnetizations are equal up to surface order corrections.

Results apply to non-interacting charged Bose gases in magnetic fields.

Abstract

Consider a charged Bose gas without self-interactions, confined in a three dimensional cubic box of side $L\geq 1$ and subjected to a constant magnetic field $B\neq 0$. If the bulk density of particles $\rho$ and the temperature $T$ are fixed, then define the canonical magnetization as the partial derivative with respect to $B$ of the reduced free energy. Our main result is that it admits thermodynamic limit for all strictly positive $\rho$, $T$ and $B$. It is also proven that the canonical and grand canonical magnetizations (the last one at fixed average density) are equal up to the surface order corrections.