The Liouville equation for singular ergodic magnetic Schrödinger operators

Abstract

We study the time evolution of a density matrix in a quantum mechanical system described by an ergodic magnetic Schrödinger operator with singular magnetic and electric potentials, the electric field being introduced adiabatically. We construct a unitary propagator that solves weakly the corresponding time-dependent Schrödinger equation, and solve a Liouville equation in an appropriate Hilbert space.

22 pages, revised with slight change in title