θ-变形双环面上的Landau问题
The Landau-Problem on the θ-Deformed Two-Torus
摘要：
我们研究了$θ$ -变形双环面上的Landau问题，并利用著名的投射模得到扰动谱。对于一个强磁场B的问题可以限制到一个特定的朗道水平。首先，我们表示生成元的代数的非交换环面作为有限维矩阵。第二种方法导致一个可约表示与$θ$依赖的中心。对于一个简单的周期势，得到了Hofstadter-butterfly谱的有理部分。
英文摘要：
We study the Landau-problem on the $θ$-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 $θ$-dependent center. For a simple periodic potential, the rational part of the Hofstadter-butterfly spectrum is obtained.
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