Bose-Einstein condensation of the magnetized ideal Bose gas

TL;DR

This paper investigates the thermodynamic behavior of a magnetized ideal Bose gas, clarifying Bose-Einstein condensation in three dimensions, and explores effects of magnetic fields, including dimensional reduction and magnetic properties.

Contribution

It provides a detailed analysis of Bose-Einstein condensation in a magnetized ideal Bose gas, including the absence of a phase transition, specific heat behavior, and effects of magnetic fields across different dimensions.

Findings

No true phase transition occurs, but a maximum in specific heat defines a critical temperature.

Large magnetic fields induce dimensional reduction to effectively one-dimensional behavior.

Magnetization and Meissner-Ochsenfeld effects are analyzed in the context of the gas.

Abstract

We study the charged non-relativistic Bose gas interacting with a constant magnetic field but which is otherwise free. The notion of Bose-Einstein condensation for the three dimensional case is clarified, and we show that although there is no condensation in the sense of a phase transition, there is still a maximum in the specific heat which can be used to define a critical temperature. Although the absence of a phase transition persists for all values of the magnetic field, we show how as the magnetic field is reduced the curves for the specific heat approach the free field curve. For large values of the magnetic field we show that the gas undergoes a "dimensional reduction" and behaves effectively as a one-dimensional gas except at very high temperatures. These general features persist for other spatial dimensions D and we show results for D=5. Finally we examine the magnetization and the Meissner-Ochsenfeld effect.