The Liouville equation for singular ergodic magnetic Schr\"odinger operators

We study the time evolution of a density matrix in a quantum mechanical system described by an ergodic magnetic Schr"odinger 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 Schr"odinger equation, and solve a Liouville equation in an appropriate Hilbert space.