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

The Liouville equation for singular ergodic magnetic Schrödinger operators