• DOI:10.1088/0031-8949/86/05/058515
• Corpus ID: 119288097

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}
}

• C. Texier
• Published 1 May 2012
• Physics
• Physica Scripta

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 shown that the slowly decaying averaged return probability of the Sinai problem, , is converted into a power-law decay, , where g is the strength of the random force field and ρ the density of absorbers.