# Ordered spectral statistics in one-dimensional disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers

@article{Texier2012OrderedSS, title={Ordered spectral statistics in one-dimensional disordered supersymmetric quantum mechanics and Sinai diffusion with dilute absorbers}, author={Christophe Texier}, journal={Physica Scripta}, year={2012}, volume={86} }

Some results on the ordered statistics of eigenvalues for one-dimensional random Schrödinger 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 non-trivial. 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…

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