Propagation of Wigner functions for the Schrödinger equation with a perturbed periodic potential
摘要：
Let V Γ be a lattice periodic potential and A and Φ 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 Schrödinger equation with Hamiltonian operator \\(H = frac{1}{2}{{( - i{{abla }_{x}} - A(\\varepsilon x))}^{2}} + {{V}_{\\Gamma }}(x) + \\phi (\\varepsilon x)\\) propagates along the flow of the semiclassical model of solid states physics up to an error of order ε . If ε -dependent corrections to the flow are taken into account, the error is improved to order ε 2 . We also discuss the propagation of the Wigner measure. The results are obtained as corollaries of an Egorov type theorem proved in [ PST3 ].
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DOI：
10.1007/978-0-8176-8202-6_17
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年份：
2004
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