 0488 Stefan Teufel and Gianluca Panati
 Propagation of Wigner functions for the Schroedinger equation with a perturbed periodic potential
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Mar 19, 04

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Abstract. Let $V_\Gamma$ be a lattice periodic potential and $A$ and
$\phi$ external electromagnetic potentials which vary slowly on the scale set by the lattice spacing.
It is shown that the Wigner function of a solution of the Schroedinger equation with Hamiltonian operator
$H = \frac{1}{2} ( i \nabla_x  A(\epsilon x) )^2 + V_\Gamma (x) + \phi(\epsilon x)$
propagates along the flow of the semiclassical model of solid states physics up an error of order $\epsilon$. If $\epsilon$dependent corrections to the flow are taken into account, the error is improved to order $\epsilon^2$.
We also discuss the propagation of the Wigner measure.
The results are obtained as corollaries of an Egorov type theorem proved in a previous paper (mp_arc 02516)
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