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Annals of Physics

Aharonov–Anandan quantum phases and Landau quantization associated with a magnetic quadrupole moment

I. C. Fonseca, K. Bakke

Published Oct 19, 2015• 28 citations
Publisher
DOI
10.1016/j.aop.2015.09.027

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Two-dimensional noncommutative atom gas with the Anandan interaction

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Landau-like quantization of the Anandan system in a special electromagnetic field is studied. Unlike the cases of the Aharonov-Casher (AC) system and the He-McKellar-Wilkens (HMW) system, the torques of the system on the magnetic dipole and the electric dipole do not vanish. By constructing Heisenberg algebra, the Landau analog levels and eigenstates on commutative space, noncommutative (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 $\ensuremath{\sigma}$ 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 labeled by $\ensuremath{\sigma}$ can be related by a supersymmetry transformation on commutative space, but the phenomenon do not 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.

arXiv:1107.5636•Physical Review A•Sep 14, 2011•2 citations
Landau-like quantization of the Anandan system in a special electromagnetic field is studied. Unlike the cases of the Aharonov-Casher (AC) system and the He-McKellar-Wilkens (HMW) system, the torques of the system on the magnetic dipole and the electric dipole do not vanish. By constructing Heisenberg algebra, the Landau analog levels and eigenstates on commutative space, noncommutative (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 $\ensuremath{\sigma}$ 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 labeled by $\ensuremath{\sigma}$ can be related by a supersymmetry transformation on commutative space, but the phenomenon do not 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.