Abstract
We investigate the leading low-energy falloff of the integrated density of states of a charged quantum particle in the Euclidean plane subject to a perpendicular constant magnetic field and repulsive impurities randomly distributed according to Poisson's law. This so-called magnetic Lifshits tail was determined by K. Broderix et al. [J. Stat. Phys. 80:1 (1995)] for algebraically decaying and by L. Erdős [Probab. Theory Relat. Fields 112:321 (1998)] for compactly supported single-impurity potentials. While the result in the first case coincides with the corresponding classical one, the Lifshits tail in Erdős' case exhibits a genuine quantum behavior. Building on both works, we determine magnetic Lifshits tails for a wide class of positive impurity potentials with a leading long-distance decay in between these limiting cases. Gaussian decay may be shown to discriminate between classical and quantum behavior. The Lifshits tail caused by Gaussian decay reveals power-law falloff with an exponent not yet completely determined.
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Hupfer, T., Leschke, H. & Warzel, S. Poissonian Obstacles with Gaussian Walls Discriminate Between Classical and Quantum Lifshits Tailing in Magnetic Fields. Journal of Statistical Physics 97, 725–750 (1999). https://doi.org/10.1023/A:1004619409967
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DOI: https://doi.org/10.1023/A:1004619409967