Convergence of Wigner Transforms in a Semiclassical Limit View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2012

AUTHORS

Luigi Ambrosio

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. More... »

PAGES

1-11

References to SciGraph publications

Book

TITLE

Nonlinear Partial Differential Equations

ISBN

978-3-642-25360-7
978-3-642-25361-4

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-25361-4_1

DOI

http://dx.doi.org/10.1007/978-3-642-25361-4_1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1033348578


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