"Spectral Theory and Mathematical Physics"
In honor of Vladimir Georgescu
Cergy-Pontoise, June 21-24, 2016.
Photo Credit: Cergy - Axe majeur,
www.cergypontoise.fr/jcms/p2_85721/fr/le-patrimoine-moderne
| Program Spyros Alexakis Kaïs Ammari Jean-Marc Bouclet Jan Derezinski Clotilde Fermanian Kammerer Christian Gérard Sylvain Golénia Dietrich Häfner Matti Lassas Mathieu Lewin Jacob Schach Moller Francis Nier Victor Nistor Benoit Pausader Main page |
Clotilde Fermanin Kammerer: Wigner measures and effective mass theorems Abstract: The dynamics of an electron in a crystal in the presence of impurities is described by a wave function that solves a semi-classical Schrödinger equation where the semi-classical parameter is the ratio between the mean spacing of the lattice and the characteristic length scale of variation of the external potential. Effective Mass Theory consists in showing that, under suitable assumptions on the initial data, the wave function can be approximated in the semi-classical limit thanks to a solution of a simpler Schrödinger equation, the effective mass equation, which is independent of the semi-classical parameter. Our goal in this talk is to describe how Wigner measure approach, conjugated with Floquet-Bloch decomposition, can be used to derive effective mass equations. We shall mainly consider two different situations depending on the geometric structure of the set of critical points of Bloch bands: when it consists of isolated points or when it is a submanifold of codimension larger than 1. These results are joint work with Victor Chabu and Fabricio Macia. |
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