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 σ 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 σ 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.
The Fock–Darwin system is studied in noncommutative quantum mechanics. We not only obtain its energy eigenvalues and eigenstates in noncommutative phase space, but also give an electron orbit description as well as the general expressions of the magnetization and the susceptibility in a noncommutative situation. Further, we discuss two particular cases of temperature and present some interesting results different from those obtained from usual quantum mechanics such as the susceptibility dependent on a magnetic field at high temperatures, the occurrence of the magnetization in a zero magnetic field and zero temperature limit, and so on.
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