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

Abstract

Consider a charged Bose gas without self-interactions, confined in a three dimensional cubic box of side $L\ge 1$ and subjected to a constant magnetic field $B\ne 0$. 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.

arXiv commentAppeared in Communications in Mathematical Physics

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