Two phases of the noncommutative quantum mechanics

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We consider quantum mechanics on the noncommutative plane in the presence of magnetic field B. We show, that the model has two essentially different phases separated by the point Bθ = ch2/e, where θ is a parameter of noncommutativity. In this point the system reduces to exactly-solvable one-dimensional system. When κ = 1 - eBθ/ch2 < 0 there is a finite number of states corresponding to the given value of the angular momentum. In another phase, i.e., when κ > 0 the number of states is infinite. The perturbative spectrum near the critical point κ = 0 is computed. © 2001 Elsevier Science B.V. All rights reserved.




Bellucci, S., Nersessian, A., & Sochichiu, C. (2001). Two phases of the noncommutative quantum mechanics. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 522(3–4), 345–349.

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