Two-dimensional Noncommutative atom Gas with Anandan interaction

TL;DR

This paper investigates the Landau quantization of the Anandan system in electromagnetic fields, exploring its eigenstates, thermodynamics, and symmetries in commutative and noncommutative spaces, revealing invariances and dualities.

Contribution

It introduces a comprehensive analysis of the Anandan system's Landau levels and thermodynamic properties in noncommutative spaces, extending previous models like AC and HMW systems.

Findings

Landau levels are invariant under noncommutative deformation.

Landau levels of Anandan system interchange under Maxwell duality.

Supersymmetry relates eigenstates in commutative space, not in NC space.

Abstract

Landau like quantization of the Anandan system in a special electromagnetic field is studied. Unlike the cases of the AC system and the HMW system, the torques of the system on the magnetic dipole and the electric dipole don't vanish. By constructing Heisenberg algebra, the Landau analog levels and eigenstates on commutative space, NC space and NC phase space are obtained respectively. By using the coherent state method, some statistical properties of such free atom gas are studied and the expressions of some thermodynamic quantities related to revolution direction are obtained. Two particular cases of temperature are discussed and the more simple expressions of the free energy on the three spaces are obtained. We give the relation between the value of $\sigma$ and revolution direction clearly, and find Landau like levels of the Anandan system are invariant and the levels between the AC system and the HMW system are interchanged each other under Maxwell dual transformations on the three spaces. The two sets of eigenstates labelled by $\sigma$ can be related by a supersymmetry transformation on commutative space, but the phenomenon don't occur on NC situation. We emphasize that some results relevant to Anandan interaction are suitable for the cases of AC interaction and HMW interaction under special conditions.