"Level spacing and Poisson statistics for continuum random Schr\""odinger operators"

Author name not available (Why is that?)

Abstract: For continuum alloy-type random Schr"odinger operators with sign-definite single-site bump functions and absolutely continuous single-site randomness we prove a probabilistic level-spacing estimate at the bottom of the spectrum. More precisely, given a finite-volume restriction of the random operator onto a box of linear size

L

, we prove that with high probability the eigenvalues below some threshold energy keep a distance of at least

for sufficiently large

. This implies simplicity of the spectrum of the infinite-volume operator below the threshold energy. Under the additional assumption of Lipschitz-continuity of the single-site probability density we also prove a Minami-type estimate and Poisson statistics for the point process given by the unfolded eigenvalues around a reference energy

E

.

Mathematics Subject Classification ID

No records found.

This page was built for publication: "Level spacing and Poisson statistics for continuum random Schr\""odinger operators"

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6503337)