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Characterization of the Metal–Insulator Transport Transition for the Two-Particle Anderson Model

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Abstract

We extend to the two-particle Anderson model the characterization of the metal–insulator transport transition obtained in the one-particle setting by Germinet and Klein. We show that, for any fixed number of particles, the slow spreading of wave packets in time implies the initial estimate of a modified version of the bootstrap multiscale analysis. In this new version, operators are restricted to boxes defined with respect to the pseudo-distance in which we have the slow spreading. At the bottom of the spectrum, within the regime of one-particle dynamical localization, we show that this modified multiscale analysis yields dynamical localization for the two-particle Anderson model, allowing us to obtain a characterization of the metal–insulator transport transition for the two-particle Anderson model at the bottom of the spectrum.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Irvine, Irvine, CA, 92697-3875, USA

    Abel Klein

  2. Coastline Community College, Newport Beach, CA, 92663, USA

    Son T. Nguyen

  3. Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Constanza Rojas-Molina

Authors
  1. Abel Klein
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  2. Son T. Nguyen
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  3. Constanza Rojas-Molina
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Corresponding author

Correspondence to Constanza Rojas-Molina.

Additional information

Communicated by Claude Alain Pillet.

A.K. was supported in part by the NSF under Grant DMS-1001509.

C.R-M. was supported in part by the European Community FP7 Programme under Grant Agreement Number 329458 and by the Collaborative Research Center 1060 from the German Research Foundation. C.R-M. acknowledges the support and hospitality of the Isaac Newton Institute for Mathematical Sciences during the program Periodic and Ergodic Spectral Problems.

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Klein, A., Nguyen, S.T. & Rojas-Molina, C. Characterization of the Metal–Insulator Transport Transition for the Two-Particle Anderson Model. Ann. Henri Poincaré 18, 2327–2365 (2017). https://doi.org/10.1007/s00023-017-0578-x

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  • DOI: https://doi.org/10.1007/s00023-017-0578-x

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