Magnetic properties of a Fermi gas in a noncommutative phase space

TL;DR

This paper investigates how noncommutative geometry affects the magnetic properties of a Fermi gas, providing explicit formulas for magnetization and susceptibility, and setting bounds on noncommutative parameters based on magnetic measurements.

Contribution

It derives explicit expressions for magnetization and susceptibility of a Fermi gas in noncommutative space, linking quantum geometry to measurable magnetic properties.

Findings

Upper bound on noncommutative parameter $ heta$ from magnetic data

Explicit formulas for Landau diamagnetism and Pauli paramagnetism in noncommutative space

Noncommutative effects influence magnetic responses of fermion gases

Abstract

Motivated by the precision attained by SQUID devices in measuring magnetic fields, we study in this article the thermodynamic behaviour of a fermion gas in two and three dimen\-sional spatial space with noncommutative coordinates and momenta. An explicit expression, both for Landau's diamagnetism and Pauli's paramagnetism, is obtained for the magnetization and magnetic susceptibility of the gas in two and three spatial dimensions. These results show that an upper bound for the noncommutative parameter $\theta\lesssim (10 \,\text{Gev})^{-2}$ could be obtained.