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Limite semi-classique de transformées de Wigner dans des milieux périodiques ou aléatoires

Abstract : This thesis is concerned with the homogenization (or semi-classical limit) of various Wigner transforms associated to L^2-bounded sequences which solve a Schrödinger equation or a first order linear hyperbolic system. Transport equations are derived for the limiting Wigner measure when a small parameter goes to zero.

A first part describes the general properties of Wigner transforms and recalls their links to pseudo-differential calculus.

A second part studies the perturbation of periodic hamiltonians by regular aperiodic potentials by means of commutation estimates concerning Bloch decompositions.

A third part studies in the weak coupling limit a class of random media which are chaotically governed by reversible dynamics but statistically governed by irreversible dynamics of Boltzmann's type.

Using the Wigner formalism a fourth part clarifies a known result of existence-unicity for the BBGKY infinite hierarchy of Schrödinger problem with N particles, when N goes to infinity, in the mean field approximation.
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Contributor : Matthieu Brassart <>
Submitted on : Wednesday, March 5, 2003 - 7:08:48 PM
Last modification on : Wednesday, October 14, 2020 - 4:24:11 AM
Long-term archiving on: : Tuesday, September 11, 2012 - 8:05:14 PM


  • HAL Id : tel-00002512, version 1



Matthieu Brassart. Limite semi-classique de transformées de Wigner dans des milieux périodiques ou aléatoires. Mathématiques [math]. Université Nice Sophia Antipolis, 2002. Français. ⟨tel-00002512⟩



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