Magnetic properties of a Fermi gas in a noncommutative phase space

Abstract

Motivated by the strong constraints to noncommutative quantum theories coming from Gamma Ray Bursts and the precision attained by SQUID devices in measuring magnetic fields, we study in this article the thermodynamic behaviour of a Fermi gas subject to the action of a background magnetic field, in two and three dimensional space with noncommutative coordinates and momenta. An explicit expression is obtained for the magnetization and magnetic susceptibility of the gas, both for Landau’s diamagnetism and Pauli’s paramagnetism. We are lead in this way to an upper bound $$\theta \lesssim (10 \,\text {Gev})^{-2}$$ for the noncommutative parameter.