TRR 12:  Symmetries and Universality in Mesoscopic Systems

Subject Area Physics
Mathematics
Term from 2003 to 2015
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 5485756
 

Project Description

The Transregional Collaborative Research Centre is a joint venture that revolves in an essential manner around the close cooperation between theoretical physicists and mathematicians. Guided by the organising principle of symmetry classes in quantum mechanics, the primary physical aim is to explore wave interference phenomena in mesoscopic systems of fermions and bosons both with and without interactions. At low temperatures, where quantum phase coherence is maintained over large distances, disorder and chaos are believed to lead to universal behaviour which is ultimately governed by the laws of random matrix theory.
A major goal of the project is to firmly establish the mechanisms underlying random matrix universality. The mathematical objects basic to this endeavour are symmetric spaces of Euclidean, compact and noncompact type, and their generalisations in the category of supermanifolds. The geometry and analysis of these spaces, and of the field theories defined over them, is to be developed. The connection with the quasiclassical physics of short wave lengths is made by studying the geometry of the associated dynamical systems, of the asymptotics emerging from trace formulas, and of limit phenomena in the representation theory of Lie groups.
DFG Programme CRC/Transregios
International Connection Poland, USA

Completed projects

Applicant Institution Universität zu Köln
Co-Applicant Institution Ludwig-Maximilians-Universität München; Ruhr-Universität Bochum; Universität Duisburg-Essen; Universität Duisburg-Essen
Campus Essen (aufgelöst)
Participating University Heinrich-Heine-Universität Düsseldorf
Participating Institution Polisch Academy of Sciences
Center for Theoretical Physics
Spokesperson Professor Dr. Alexander Altland