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

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

• A01 - Effective theories of correlated fermions (Project Heads von Delft, Jan ;  Efetov, Konstantin ;  Müller, Peter )
• A02 - Random lasers (Project Head Haake, Fritz )
• A03 - Nonlinear Dynamics of Strongly Interacting Quantum Fields (Project Heads Kehrein, Stefan ;  Kunze, Markus ;  Rosch, Achim ;  Schützhold, Ralf )
• A03 - Nonlinear Dynamics of Strongly Interacting Quantum Fields (Project Head Hornberger, Klaus )
• A04 - Nonequilibrium phenomena (Project Heads Egger, Reinhold ;  Kehrein, Stefan ;  Schützhold, Ralf )
• A05 - Mesoscopic transport of Dirac fermions (Project Heads Efetov, Konstantin ;  Egger, Reinhold ;  Eremin, Ilya )
• A06 - Mathematical theory of disordered systems with interactions (Project Heads Erdös, Ph.D., Laszlo ;  Kirsch, Werner )
• A07 - Fluctuations and large deviations in nonequilibrium stochastic dynamics (Project Heads Altland, Alexander ;  Frey, Erwin ;  Krug, Joachim ;  Külske, Christof ;  Winter, Anita )
• A08 - Non-abelian symmetries in tensor networks (Project Heads von Delft, Jan ;  Littelmann, Peter ;  Schollwöck, Ulrich )
• A09 - The spectrum of interacting fermions in graphene quantum dots (Project Heads Egger, Reinhold ;  Siedentop, Heinz ;  Stockmeyer, Edgardo )
• B01 - Hyperbolic dynamical systems, periodic orbits and quantum spectra (Project Heads Altland, Alexander ;  Guhr, Karl Thomas ;  Haake, Fritz ;  Knieper, Gerhard ;  Kunze, Markus )
• B02 - Limits of representations (Project Heads Huckleberry, Alan T. ;  Kus, Marek ;  Littelmann, Peter ;  Marinescu, George Teodor ;  Winkelmann, Jörg )
• B03 - Ballistic sigma models (Project Heads Altland, Alexander ;  Efetov, Konstantin ;  Haake, Fritz )
• C01 - Dirac Operators: their role in mesoscopic physics and their sprectral theory (Project Heads Altland, Alexander ;  Lesch, Matthias ;  Zirnbauer, Martin R. )
• C02 - Fluctuations and universality of invariant random matrix ensembles (Project Heads Dette, Holger ;  Eichelsbacher, Peter ;  Erdös, Ph.D., Laszlo )
• C03 - The universality question for disordered low-frequency bosons (Project Heads Heinzner, Peter ;  Huckleberry, Alan T. ;  Zirnbauer, Martin R. )
• C04 - Random matrices in chotic or complex systems (Project Heads Guhr, Karl Thomas ;  Klesse, Rochus ;  Schützhold, Ralf ;  Zyczkowski, Ph.D., Karol )
• C05 - Dynamics on disordered graphs (Project Heads Krug, Joachim ;  Lässig, Michael )
• C06 - Single-particle operators with disorder of short range structure (Project Heads Kirsch, Werner ;  Kriecherbauer, Thomas ;  Siedentop, Heinz )
• C06 - Systems with short range disorder and glassy correlations (Project Heads Eichelsbacher, Peter ;  Erdös, Ph.D., Laszlo ;  Külske, Christof )
• D01 - Transfer versus scattering in the symmetry classes (Project Heads Heinzner, Peter ;  Huckleberry, Alan T. ;  Zirnbauer, Martin R. )
• D02 - Developing and applying the theory of symmetric and symplectic supermanifolds (Project Heads Alldridge, Alexander ;  Guhr, Karl Thomas ;  Heinzner, Peter ;  Wurzbacher, Tilmann )
• D03 - Level dynamics (Project Heads Huckleberry, Alan T. ;  Kus, Marek ;  Thorbergsson, Gudlaugur )
• D04 - Howe pairs, Fock representations, and conformal fields (Project Heads Huckleberry, Alan T. ;  Püttmann, Annett ;  Quella, Thomas ;  Winkelmann, Jörg ;  Zirnbauer, Martin R. )
• N01 - NN (Project Head Warzel, Simone )
• Z - Central Tasks (Project Head Altland, Alexander )

• 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