Analysis of quantum many-particle operators with disorder

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The goal of this project is to address fundamental issues in the analysis of random quantum many-particle operators. So far, most of the mathematical research in the field of random operators has been focused on the spectral theory of random single-particle operators. A key theorem here addresses localization for large disorder: any given interval of the almost-sure spectrum belongs to the pure point spectrum provided the randomness is large enough; the corresponding eigenfunctions are exponentially localized. The PI's research program aims to investigate the fate of this strong localization regime in the interacting case. The influence of many-particle correlations will be examined for both fermionic and bosonic systems.Random quantum many-particle operators arise in models of semiconductors, dirty superconductors, or Bose-Einstein condensates in disordered media. In such systems, the interplay between quantum and statistical fluctuations due to the disorder gives rise to interesting physical phenomena like the suppression of electronic transport or of Bose-Einstein condensation. The mathematical study of these phenomena involves combining techniques from different areas of mathematics, in particular, functional analysis and probability.