Program
on Nonlinear Schrödinger and Quantum Boltzmann Equations: 2001
| Winter School on Nonlinear Schrödinger Equations | February 5-16, 2001 |
| Workshop on Nonlinear Dispersive Equations | July 17-24, 2001 |
| Summer School on Nonlinear Schrödinger Equations | July 25 - Aug 10, 2001 |
| Twin Colloquium: Paris Vienna on Hydrodynamical limits: results and perspectives |
Paris: September 24-28 Vienna: October 22-24 |
| Workshop on Semiclassical limits: WKB methods vs Wigner transform methods | November 22 - 25, 2001 |
| Colloquium on Asymptotic Analysis of the Dirac-Maxwell system | December 10 - 14, 2001 |
This program in partial differential equations and mathematical physics focuses on nonlinear Schrödinger equations (NLS) and quantum kinetic equations. These fields of research (i.e., NLS and related dispersive phenomena, and quantum transport theory) are very active ones with many applications.
A powerful new technique in these fields is the Wigner transform. The crucial point is that taking the Wigner transform effects a transition from configuration space to a position-momentum "phase space", resulting in a kinetic formulation of the PDEs. In recent years the Wigner transform has shown itself to be a perfect tool for taking semiclassical limits and it replaces the WKB approach for certain classes of problems. The latter runs into severe problems at "caustics," which are somehow "unfolded" in the phase-space approach. The particluar advantage of the Wigner transform in this respect has been seen, for example, in the case of the rigorous semiclassical limit for the quantum hydrodynamic model for semiconductors.
We will be considering certain state-of-the-art problems in the field of Nonlinear Schrödinger equations, trying to apply the Wigner formalism to the semiclassical limits of the problems of the type of the defocusing (and focusing) NLS equations. We will also be considering applications of the Wigner formalism to the Dirac-Maxwell model (the Dirac equation coupled to Maxwell's equations for the electomagnetic field) and the Pauli equation with self-consistent coupling.
Another of our objectives is to consistently incorporate quantum scattering into kinetic quantum transport models. We shall concern ourselves with existence, uniqueness, and asymptotic properties of solutions to various quantum kinetic models: N-particle Schrödinger equations, quantum Fokker-Planck equations, the second quantization approach for phonon scattering, and random potential approaches. It is hoped that some light may be shed on the famous fundamental question of how irreversible equations may be derived from reversible models.
Workshop on Asymptotic Analysis of the Dirac-Maxwell systemESI and WPI ViennaDECEMBER 10 - 14, 2001 Organized by N.J. Mauser, G. Rein, and S. Selberg
This workshop is a gathering of several international working groups
who work on (quantum) relativistic (kinetic) models.
Particular emphasis is given to the connection of models via
asymptotic analysis e.g. in a hierarchy of models for charged particles
that spans from the Dirac-Maxwell system to the Euler equations.
ParticipantsH. Andreasson, P. Bechouche, Y. Brenier, F. Chalub, K. Fellner, A. Gottlieb, V. Imaikin, S. Kamvissis, A. Komech, M. Kunzinger, H. Li, N. Masmoudi, N.J. Mauser, J. Mayorga, L. Neumann, C. Pallard, M. Puel, G. Rein, A. Rendall, S. Selberg, Wang Shu, C. Sparber, R. Steinbauer, H.P. StimmingSchedule (all talks in ESI lecture hall):
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