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Landau quantum systems: an approach based on symmetry
J. Negro, M. A. del Olmo, A. Rodriguez-Marco
abstract: We show that the Landau quantum systems (or integer quantum Hall effect
systems) in a plane, sphere or a hyperboloid, can be explained in a complete
meaningful way from group-theoretical considerations concerning the symmetry
group of the corresponding configuration space. The crucial point in our
development is the role played by locality and its appropriate mathematical
framework, the fiber bundles. In this way the Landau levels can be understood
as the local equivalence classes of the symmetry group. We develop a unified
treatment that supplies the correct geometric way to recover the planar case as
a limit of the spherical or the hyperbolic quantum systems when the curvature
goes to zero. This is an interesting case where a contraction procedure gives
rise to nontrivial cohomology starting from a trivial one. We show how to
reduce the quantum hyperbolic Landau problem to a Morse system using horocyclic
coordinates. An algebraic analysis of the eigenvalue equation allow us to build
ladder operators which can help in solving the spectrum under different
boundary conditions.
- oai_identifier:
- oai:arXiv.org:quant-ph/0110152
- categories:
- quant-ph
- comments:
- LaTeX2e, 32 pages, 10 figures
- doi:
- 10.1088/0305-4470/35/9/317
- arxiv_id:
- quant-ph/0110152
- created:
- 2001-10-26
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