Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers

  title={Ordered spectral statistics in 1D disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers},
  author={Christophe Texier},
  journal={arXiv: Disordered Systems and Neural Networks},
  • C. Texier
  • Published 1 May 2012
  • Physics, Mathematics
  • arXiv: Disordered Systems and Neural Networks
Some results on the ordered statistics of eigenvalues for one-dimensional random Schrodinger Hamiltonians are reviewed. In the case of supersymmetric quantum mechanics with disorder, the existence of low energy delocalized states induces eigenvalue correlations and makes the ordered statistics problem nontrivial. The resulting distributions are used to analyze the problem of classical diffusion in a random force field (Sinai problem) in the presence of weakly concentrated absorbers. It is shown… 

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