Mathematical Physics Seminar

MATHEMATICAL PHYSICS SEMINAR

Spring 2007 Lectures

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

Date	Speaker	Title
Feb. 20	Daniel Lenz, TU Chemnitz	Aperiodic order and pure point diffraction We give an introduction into the mathematical diffraction theory of aperiodic order. We then focus on the relationship between the diffraction spectrum and the spectrum of the associated dynamical system. Finally, we discuss a method of calculating intensities of Bragg peaks via a Wiener/Wintner type ergodic theorem. Part of this talk is based on joint work with Michael Baake and Nicolae Strungaru respectively.
Feb. 27	Jakob Yngvason, University of Vienna	The Thomas-Fermi limit of rapidly rotating Bose gases Starting from the many-body Hamiltonian we derive the leading order energy and density asymptotics for the ground state energy and density of a rotating Bose gas in an anharmonic trap, in the limit in which the coupling parameter and/or the rotation speed tend to infinity, but the gas remains dilute. Although the many-body wave function is expected to have a complicated phase, the leading order contribution to the energy can be computed by minimizing a simple functional of the density alone.
Apr. 3	Christian Stucchio, Rutgers University	Laser-Atom Interaction: Ionization and Resonances for a model system The behavior of an atom in a radiation field is a topic of fundamental importance in atomic physics. Except for a few limiting regimes (radiation is small, radiation is slowly varying), very little is known rigorously about the the time-dependent behavior of the electron's wavefunction. present a new method for analyzing the problem, based on domain restriction using Dirichlet-to-Neumann boundary conditions. As an application, I show that ionization always occurs (regardless of the frequency, or field strength) in a common physical model. This is a joint work with O. Costin and J. L. Lebowitz.
Apr. 17	Vojkan Jaksic, McGill University	Recent Developments in Non-Equilibrium Quantum Statistical Mechanics: An Overview In this talk I shall discuss mathematical foundations of non-equilibrium quantum statistical mechanics focusing on a class of recent developments which fall roughly into two categories: (A) Axiomatic results that concern mathematical structure of the theory; (B) Study of concrete physically relevant models; In the first part of the talk I shall focus on (A) and discuss the entropy production observable, entropy production balance equation, non-equilibrium steady states and linear response theory (Kubo formulas, Onsager relations) within the framework of algebraic quantum statistical mechanics. In the second part of the talk I will discuss some concrete physically relevant models for which the axioms of (A) can be verified.
Note special date: Thurs., May 3	Anton Bovier, TU-Berlin and WIAS	Universality of Ageing in Mean Field Spin Glasses ``Ageing'' has become a commonly used concept to characterize the slow-down of long-term dynamics in many complex systems, notably glasses and spin-glasses. It is manifest in scaling properties of time-time correlation functions. A simple exactly solvable toy model which exhibits ageing is the so-called REM-like trap modes, a simple Markov chain with random transition rates with a heavy-tailed distribution. It is believed that this simple model describes correctly the ageing in a large class of more realistic models. In this talk I will present results, obtained in collaboration with G. Ben Arous and J. Cerny, confirming this expectation for a class of Glauber dynamics of p-spin interaction mean-field spin-glass models.
Note special date and time: Fri., May 4, 1:30 p.m.	Francois Germinet Univ. Cergy-Pontoise	Anderson localization for random Schroedinger operators We shall review some recent developments on localization exhibited by large classes of random operators. In particular, localization in presence of an Anderson potential with an arbitrary non degenerate underlying probability law is proved.