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Convergence of Wigner Transforms in a Semiclassical Limit

  • Luigi Ambrosio
Part of the Abel Symposia book series (ABEL, volume 7)

Abstract

We prove convergence of the Wigner transforms of solutions to the Schrödinger equation, in a semiclassical limit, to solutions to the Liouville equation. We are able to include in our convergence result rough or singular potentials (with Coulomb repulsive singularities), provided convergence is understood for “almost all” initial data. The rigorous statement involves a suitable extension of the DiPerna–Lions theory to the infinite-dimensional space of probability measure, where both the Wigner and the Liouville dynamics can be read.

Keywords

Convergence Result Liouville Equation Semiclassical Limit Uniform Decay Operator Inequality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Scuola Normale SuperiorePisaItaly

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