dorsal/arxiv
View SchemaThe Landau-Problem on the \theta-Deformed Two-Torus
| Authors | H. Grosse, M. Kornexl |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0210042 |
| URL | https://arxiv.org/abs/quant-ph/0210042 |
| Journal | Lett.Math.Phys. 63 (2003) 73-83 |
Abstract
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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"abstract": "We study the Landau-problem on the $\\theta$-deformed two-torus and use\nwell-known projective modules to obtain perturbed spectra. For a strong\nmagnetic field B the problem can be restricted to one particular Landau-level.\nFirst we represent generators of the algebra of the non-commutative torus as\nfinite dimensional matrices. A second approach leads to a reducible\nrepresentation with a $\\theta$-dependent center. For a simple periodic\npotential, the rational part of the Hofstadter-butterfly spectrum is obtained.",
"arxiv_id": "quant-ph/0210042",
"authors": [
"H. Grosse",
"M. Kornexl"
],
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"quant-ph",
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],
"journal_ref": "Lett.Math.Phys. 63 (2003) 73-83",
"title": "The Landau-Problem on the \\theta-Deformed Two-Torus",
"url": "https://arxiv.org/abs/quant-ph/0210042"
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