Thermodynamics of a charged particle in a noncommutative plane in a background magnetic field

TL;DR

This paper explores the thermodynamics of a charged particle in a noncommutative plane under a magnetic field, revealing modifications in susceptibility and magnetization oscillations due to spatial noncommutativity, with results valid to all orders in the noncommutative parameter.

Contribution

It introduces a method to analyze the Landau system in noncommutative space using Seiberg-Witten map and Bopp-shift, providing new insights into noncommutative effects on thermodynamic properties.

Findings

Non-zero susceptibility for magnetic fields above a threshold in noncommutative space.

Magnetization oscillations are corrected by noncommutative parameters.

Results are valid to all orders in the noncommutative parameter .

Abstract

Landau system in noncommutative space has been considered. To take into account the issue of gauge invariance in noncommutative space, we incorporate the Seiberg-Witten map in our analysis. Generalised Bopp-shift transformation is then used to map the noncommutative system to its commutative equivalent system. In particular we have computed the partition function of the system and from this we obtained the susceptibility of the Landau system and found that the result gets modified by the spatial noncommutative parameter $\theta$. We also investigate the de Hass--van Alphen effect in noncommutative space and observe that the oscillation of the magnetization and the susceptibility gets noncommutative corrections. Interestingly, the susceptibility in the noncommutative scenario is non-zero in the range of the magnetic field greater than the threshold value which is in contrast to its commutative counterpart. The results obtained are valid upto all orders in the noncommutative parameter $\theta$.