The University of Texas at Austin

2012/13 Focus on Quantum Transport

2013/14 Thematic Program on Quantum Transport.

With focus on research, and on the training of graduate and advanced undergraduate students, from a multidisciplinary, integrative perspective. The topics complement a graduate course on analytical aspects of Quantum Theory taught in Fall 2013.

Schedule of Events

Minicourses: Survey and Research Talks

Advanced minicourses consisting of survey and research talks by experts in their respective fields.

Tentative list of Speakers:

Fall 2013

Israel Michael Sigal, University of Toronto. Talk on Oct 23, 2013.
      Magnetic Vortices, Nielsen-Olesen - Nambu strings and theta functions.

Spring 2014

Constanze Liaw, Baylor University. Talk on Feb 3, 2014
      Cyclic vectors for rank one perturbations and Anderson-type Hamiltonians

Christof Sparber, University of Illinois at Chicago. Talks on Feb 17 and 19, 2014
      Dispersive blow-up for nonlinear Schroedinger type equations
      On Wigner and Bohmian measures in semiclassical quantum dynamics

Irina Nenciu, University of Illinois at Chicago. Talks on Feb 17 and 19, 2014
      On confinement and essential self-adjointness for Schroedinger operators
      Completely integrable systems and their connections within mathematics

James Colliander, University of Toronto. Talk on April 11, 2014
      Big frequency cascades in the nonlinear Schroedinger evolution

Introductory and survey talks, held by graduate students.

Graduate Talks:

Kenny Taliaferro, UT Austin. Talk on Nov 15, 2013.
      The Quantum de Finetti Theorem.

Multidisciplinary Perspective

In this thematic year, we focus on the transport of energy and mass in nonlinear quantum systems. The topics include semiclassical analysis via Wigner transforms; frequency cascades in NLS; the stability of lattice solutions in superconductors; the numerical analysis of quantum systems where transport is absent (Anderson localization).

We mainly emphasize aspects of the following disciplines:

PDE theory

Key concepts and results connected to the analytic and PDE theory of mass and energy transport in quantum dynamics. Survey of recent advances.

Mathematical Physics

Link between microscopic and macroscopic physics, lattice formation in systems of Cooper pairs with links to modular functions.

Computational Simulations

Numerical study of transport properties of quantum systems currently beyond grasp in PDE theory. Predictions from numerical simulations, and key problems in numerical analysis.

Program Information

This is the second in a series of five thematic years held at the Department of Mathematics, centered around a single equation or method, viewed from an integrative, multidisciplinary perspective encompassing nonlinear PDE's, mathematical physics, and computational simulations.

Focus topics addressed in these thematic years tentatively include nonlinear Schrodinger equations, wave propagation in random media, Vlasov and Boltzmann equations, Euler equations, and multiscale and renormalization group methods. The mathematical physics component will address the derivation of these equations from quantum dynamics.

Some of the main educational goals are:
  • To provide graduate students in analysis, applied mathematics, and mathematical physics with an broad insight into areas close to their research fields.

  • To help advanced undergraduate students compare the styles of research in various disciplines, possibly to identify directions for their future studies.
Presentations and lectures will be held by experts in pure and applied mathematics, physics, and engineering, invited from UT Austin and other institutions.

This program is supported by the NSF CAREER grant DMS-1151414.
Organizer: Thomas Chen.