非对易Landau问题的手征分解(英文)

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In two remarkable papers Alvarez et al.[1]pointed out that two uncoupled 1dchiral oscillators yield,when combined,an interesting non-commutative system in the plane.The purely-magnetic“exotic”Landau problem(NCLP)can,in particular,be obtained for a suitable choice of the parameters.The inclusion of the electric field which,for non-commutative particles,also induces an anomalous velocity term(missed in Ref.[1]),is important,though,in the study of a Bloch electron,and for both the ordinary and the anomalous Hall effects,for example. In two remarkable papers Alvarez et al. [1] pointed out that two uncoupled 1dchiral oscillators yield, when combined, an interesting non-commutative system in the plane. Purely magnetic “exotic” Landau problem (NCLP) can, in particular, be obtained for a suitable choice of the parameters. inclusion of the electric field which, for non-commutative particles, also induces an anomalous velocity term (missed in Ref. [1]), is important, though, in the study of a Bloch electron, and for both the ordinary and the anomalous Hall effects, for example.
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