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Landau like quantization of the Anandan system in a special electromagneticfield is studied. Unlike the cases of the AC system and the HMW system, thetorques of the system on the magnetic dipole and the electric dipole don'tvanish. By constructing Heisenberg algebra, the Landau analog levels andeigenstates on commutative space, NC space and NC phase space are obtainedrespectively. By using the coherent state method, some statistical propertiesof such free atom gas are studied and the expressions of some thermodynamicquantities related to revolution direction are obtained. Two particular casesof temperature are discussed and the more simple expressions of the free energyon the three spaces are obtained. We give the relation between the value of$\sigma$ and revolution direction clearly, and find Landau like levels of theAnandan system are invariant and the levels between the AC system and the HMWsystem are interchanged each other under Maxwell dual transformations on thethree spaces. The two sets of eigenstates labelled by $\sigma$ can be relatedby a supersymmetry transformation on commutative space, but the phenomenondon't occur on NC situation. We emphasize that some results relevant to Anandaninteraction are suitable for the cases of AC interaction and HMW interactionunder special conditions.

Two-dimensional Noncommutative atom Gas with Anandan interaction