Propagation of Wigner Functions for the Schrödinger Equation with a Perturbed Periodic Potential

  • S. Teufel
  • G. Panati
Conference paper
Part of the Trends in Mathematics book series (TM)


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 \(H = \tfrac{1}{2}{{( - i{{\nabla }_{x}} - A(\varepsilon x))}^{2}} + {{V}_{\Gamma }}(x) + \phi (\varepsilon x)\) 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].


Wigner Function Schrodinger Equation Semiclassical Limit Anomalous Hall Effect Semiclassical Model 
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Copyright information

© Springer Basel AG 2004

Authors and Affiliations

  • S. Teufel
    • 1
  • G. Panati
    • 1
  1. 1.Zentrum MathematikTechnische Universität MünchenMünchenGermany

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