Anderson localization in the multi-particle tight-binding model at low energies or with weak interaction

Details Anderson localization in the multi-particle tight-binding model at low energies or with weak interaction Anderson localization in the multi-particle tight-binding model at low energies or with weak interaction

2012-01-11

arxiv.org/abs/1201.2339v1

Physics

Mathematical Physics

Scientific paper

We consider the multi-particle lattice Anderson model with an i.i.d. random external potential and a short-range interaction. Using the multi-particle multiscale analysis (MPMSA) developed by Chulaevsky and Suhov (2009), we prove spectral localization for such Hamiltonians at low energies under the assumption of log-H\"{o}lder continuity of the marginal probability distribution of the random potential. Under a stronger assumption of H\"older continuity, Anderson localization for such systems at low energies was established earlier by Aizenman and Warzel (2009) with the help of the multi-particle Fractional-Moment Method.

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