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Schrödinger Operators with Random \(\delta \) Magnetic Fields

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Abstract

We shall consider the Schrödinger operators on \(\mathbb {R}^2\) with random \(\delta \) magnetic fields. Under some mild conditions on the positions and the fluxes of the \(\delta \)-fields, we prove the spectrum coincides with \([0,\infty )\) and the integrated density of states (IDS) decays exponentially at the bottom of the spectrum (Lifshitz tail), by using the Hardy-type inequality by Laptev-Weidl (Oper Theory Adv Appl 108:299–305, 1999). We also give a lower bound for IDS at the bottom of the spectrum.

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Authors and Affiliations

  1. Faculty of Arts and Sciences, Kyoto Institute of Technology, Matsugasaki, Sakyo-ku, Kyoto, 606-8585, Japan

    Takuya Mine

  2. Graduate School of Material Science, University of Hyogo, Shosha, Himeji, 671-2280, Japan

    Yuji Nomura

Authors
  1. Takuya Mine
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  2. Yuji Nomura
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Correspondence to Yuji Nomura.

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Communicated by Jean Bellissard.

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Mine, T., Nomura, Y. Schrödinger Operators with Random \(\delta \) Magnetic Fields. Ann. Henri Poincaré 18, 1349–1369 (2017). https://doi.org/10.1007/s00023-017-0559-0

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  • DOI: https://doi.org/10.1007/s00023-017-0559-0

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