MATHEMATICAL PHYSICS SEMINAR

Department of Mathematics
Princeton University
Princeton University Department of Mathematics Seminars Fall 2009 Schedule


FALL 2009 Lectures

Regular meeting time: Tuesdays 4:30--5:30
Place: Jadwin 343

Date Speaker Title
Nov. 10 Mathieu Lewin,
Université de Cergy-Pontoise

A variational model for crystals with defects
This talk will be devoted to the reduced Hartree-Fock model for crystals with defects.

The main idea is to describe at the same time the electrons bound by the defect and the (nonlinear) behavior of the infinite crystal. This leads to a bounded-below nonlinear functional whose variable is however an operator of infinite-rank.

I will provide the correct functional setting for this functional, state the existence of global-in-time solutions to the associated time-dependent Schrödinger equation, and discuss the existence, the properties and the stability of bound states. In particular I will define the dielectric permittivity of the perfect crystal and relate this to some properties of ground states.

This is a review of joint works with Eric Cancès and Amélie Deleurence (Ecoledes Ponts, Paris).

Nov. 17 Jakob Yngvason,
University of Vienna

The emergence of a giant vortex in a fast rotating Bose gas.
A Bose gas in fast rotation normally exhibits a growing number of vortices of unit strength if the angular velocity is increased. In an anharmonic trap at sufficiently high velocity, however, a phase transition is expected: Vortices in the bulk should disappear and all vorticity become concentrated in a region where the density is very low. Moreover, the critical velocity for the transition is expected to increase with on the interaction strength in a definite manner. In the lecture rigorous results on this behavior within two-dimensional Gross-Pitaevskii theory will be presented. This is joint work with Michele Correggi and Nicolas Rougerie.
Nov. 24 Alexander Sodin,
Tel Aviv Univ.
The spectral edge of random band matrices
We consider random periodic N X N band matrices of band width W.
If the band is wide (W >> N^{5/6}), the spectral statistics at the edge behave similarly to those of GUE matrices; in particular, the largest eigenvalue converges in distribution to the Tracy -- Widom law. Otherwise, a different limit appears. The results are consistent with the Thouless criterion for localization, adapted to the band matrix setting by Fyodorov and Mirlin.
Dec. 1 Vieri Mastropietro,
Univ. Rome II
TBA
     

 

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For more information about this seminar, contact Princeton University Department of Mathematics Seminar