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Anderson localization for two interacting quasiperiodic particles

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Abstract

We consider a system of two discrete quasiperiodic 1D particles as an operator on \(\ell^2(\mathbb Z^2)\) and establish Anderson localization at large disorder, assuming the potential has no cosine-type symmetries. In the presence of symmetries, we show localization outside of a neighborhood of finitely many energies. One can also add a deterministic background potential of low complexity, which includes periodic backgrounds and finite range interaction potentials. Such background potentials can only take finitely many values, and the excluded energies in the symmetric case are associated to those values.

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Authors and Affiliations

  1. School of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540, USA

    Jean Bourgain

  2. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Ilya Kachkovskiy

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  1. Jean Bourgain
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  2. Ilya Kachkovskiy
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Correspondence to Ilya Kachkovskiy.

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Bourgain, J., Kachkovskiy, I. Anderson localization for two interacting quasiperiodic particles. Geom. Funct. Anal. 29, 3–43 (2019). https://doi.org/10.1007/s00039-019-00478-4

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  • DOI: https://doi.org/10.1007/s00039-019-00478-4

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