Abstract

We propose a simple construction of the Anderson Hamiltonian with white noise potential on ${ℝ}^2$ and ${ℝ}^3$ based on the solution theory of the parabolic Anderson model. It relies on a theorem of Klein and Landau (1981) that associates a unique self-adjoint generator to a symmetric semigroup satisfying some mild assumptions. Then, we show that almost surely the spectrum of this random Schrödinger operator is $ℝ$. To prove this result, we extend the method of Kotani (1985) to our setting of singular random operators.

Keywords

Mathematical Subject Classification

Milestones

Authors