Two-dimensional Noncommutative atom Gas with Anandan interaction

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.

Latex, 10 pages

References in corpus (9)

• Landau Levels Analog to Electric Dipole
• The Aharonov-Bohm Effect in Noncommutative Quantum Mechanics
• Representation of noncommutative phase space
• Nonrelativistic anyons in external electromagnetic field
• The Noncommutative Anandan's Quantum Phase
• Landau Analog Levels for Dipoles in the Noncommutative Space and Phase Space
• Quantum Hall Effect In Bilayer Systems And The Noncommutative Plane: A Toy Model Approach
• The Aharonov-Casher effect for spin-1 particles in non-commutative quantum mechanics
• The He-McKellar-Wilkens effect for spin one particles in non-commutative quantum mechanics

Cited by in corpus (2)

• Noncommutative Brownian motion
• Charged Dirac fermions with anomalous magnetic moment in the presence of the chiral magnetic effect and of a noncommutative phase space