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Project Area A: Many-Body Phenomena

Project Area B: Semiclassical Asymptotics

Project Area C: Effective Single-Particle Systems beyond Wigner Dyson

Project Area D: Symmetry Classes and Symmetric Spaces

Project Area C: Effective Single-Particle Systems beyond Wigner Dyson

C2

Fluctations and universality of random matrix esembles
H. Dette , M Bochum, P. Eichelsbacher, M Bochum, L. Erdös, M München
We investigate universality and fluctuation properties of matrix ensembles. We will consider those types of random matrices that are most relevant for the purposes of the SFB/TR, i.e. Wigner ensembles and matrix ensembles of invariant, block, res. sparse type. The main objects of interest will be densities of eigenvalues, local eigenvalue statistics as well as determinantal point processes. In our investigation we will use in particular the hydrodynamical approach of Erdös et al, the method of orthogonal polynomials and Stein's method.

C3

The universality question for disordered low-frequency bosons
P. Heinzner, M Bochum, A. Huckleberry, M Bochum, M. Zirnbauer, TP Köln
While we do understand the heuristics of disorder, symmetries, and universality rather well for the case of fermionic quasiparticles, the corresponding questions for bosons are still open. In our quest for a good and tractable random matrix model of disordered bosonic excitations (examples are harmonic vibrations of an amorphous solid, or spin waves in a disordered magnet) we are studying invariant probability measures as well as band matrices supported on the cone of elliptic elements (i.e., the generators of stable motions) inside a noncompact Lie algebra.

C4

Random matrics in chaotic and complex systems
T. Guhr, TP Duisburg-Essen, R. Klesse, TP Köln, R. Schützhold, TP Duisburg-Essen, K. Zyczkowski, CTP Warsaw
We are interested in correlations and distributions in quantum chaotic scattering. We determine the moments of conductance and shot noise power in chaotic cavities. Furthermore we investigate other random matrix problems and the statistics of bistochastic matrices and quantum operations.

C6

Single particle operators with disorder of short range structure
P. Eichelsbacher, M Bochum, L. Erdös, M München, C. Külske, M Bochum
Part of project C6 is devoted to the mathematical understanding of the transport properties of graphene which is a single planar sheet of carbon atoms that are densely packed in a honeycomb crystal lattice. The picture shows the spectral band structure at the linear crossing that is responsible for the unusual transport properties of graphene
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