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Recent progress in the multi-patricle Anderson tight binding model

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The Anderson model is a Schroedinger operator with a random potential. It is used in several areas of physics to describe quantum systems with impurities. The main question here is about the character of the spectrum of such an operator; the main issue is pure point (insulation) versus absolutely continuous (conductivity). The Anderson tight binding model is set on a lattice, and a standard assumption about the potential is IID . The model generated a vast literature but so far it was almost exclusively about a single-particle system. Recently, Chulaevski and myself started a project aiming multi-particle systems. I’ll report on our progress so far. No preliminary knowledge of quantum mechanics or spectral theory will be assumed.

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