The Liouville equation for singular ergodic magnetic Schrödinger operators

Details The Liouville equation for singular ergodic magnetic Schrödinger operators The Liouville equation for singular ergodic magnetic Schrödinger operators

2008-11-24

arxiv.org/abs/0811.3960v2

Physics

Mathematical Physics

22 pages, revised with slight change in title

Scientific paper

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.

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