On the Schrodinger operator with white noise potential

Cyril Labbé

This talk will focus on the random Schrodinger operator on R obtained by perturbing the Laplacian with a white noise. First, I will present an Anderson localization result for this operator: the spectrum is pure point and the eigenfunctions exponentially localized. Second, I will present various results on the eigenvalues and eigenfunctions of the finite-volume approximation of this operator in the infinite volume limit: it turns out that many different behaviors can be observed according to the energy regime one focuses on. This is based on a series of joint works with Laure Dumaz.

Slides