On two-particle Anderson localization at low energies

Abstract

We prove exponential spectral localization in a two-particle lattice Anderson model, with a short-range interaction and external random i.i.d. potential, at sufficiently low energies. The proof is based on the multi-particle multi-scale analysis developed earlier by Chulaevsky and Suhov (2009) in the case of high disorder. Our method applies to a larger class of random potentials than in Aizenman and Warzel (2009) where dynamical localization was proved with the help of the fractional moment method.

References in corpus (4)

• Wegner bounds for a two-particle tight binding model
• Eigenfunctions in a two-particle Anderson tight binding model
• A Wegner estimate for multi-particle random Hamiltonians
• On two-particle Anderson localization at low energies

Cited by in corpus (12)

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• On two-particle Anderson localization at low energies
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• Multi-particle localization at low energy for the multi-dimensional continuous Anderson model
• Lifshitz tails for the multi-particle continuous Anderson model
• On complete localization for the one-dimensional multi-particle Anderson-Bernoulli model with infinite range interaction
• Localization for one-dimensional two-particle random Schrödinger operators with Poisson potential
• Resonances and multi-particle localization at low energy
• Conditional distribution of the sample mean and localization
• Wegner bounds for one-dimensional multi-particle Bernoulli-Anderson models in the continuum
• Wegner bounds for N-body interacting Bernoulli-Anderson models in one dimension
• Localization for $N$-particle continuous models with strongly mixing correlated random potentials