The Landau-Problem on the θ-Deformed Two-Torus

Details The Landau-Problem on the θ-Deformed Two-Torus The Landau-Problem on the θ-Deformed Two-Torus

2002-10-07

arxiv.org/abs/quant-ph/0210042v1

Lett.Math.Phys. 63 (2003) 73-83

Physics

Quantum Physics

11 pages, 3 figures

Scientific paper

We study the Landau-problem on the $\theta$-deformed two-torus and use well-known projective modules to obtain perturbed spectra. For a strong magnetic field B the problem can be restricted to one particular Landau-level. First we represent generators of the algebra of the non-commutative torus as finite dimensional matrices. A second approach leads to a reducible representation with a $\theta$-dependent center. For a simple periodic potential, the rational part of the Hofstadter-butterfly spectrum is obtained.

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