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The Non-commutative Landau Problem

✍ Scribed by P.A. Horváthy

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
119 KB
Volume
299
Category
Article
ISSN
0003-4916

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✦ Synopsis

The Landau problem is discussed in two similar but still different non-commutative frameworks. The "standard" one, where the coupling to the gauge field is achieved using Poisson brackets, yields all Landau levels. The "exotic" approach, where the coupling to the gauge field is achieved using the symplectic structure, only yields lowest-Landau level states, as advocated by Peierls and used in the description of the ground states of the fractional quantum Hall effect. The same reduced model also describes vortex dynamics in a superfluid 4 He film. Remarkably, the spectrum depends crucially on the quantization scheme. The system is symmetric w.r.t. area-preserving diffeomorphisms.

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