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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 B: Semiclassical Asymptotics

B1

Hyperbolic dynamical systems, periodic orbits and quantum spectra
A. Altland, TP Köln, T. Guhr, TP Duisburg-Essen, F. Haake , TP Duisburg-Essen, G. Knieper , M Bochum, M. Kunze M Köln
The project aims at understanding universal classical and quantum properties of fully chaotic dynamics. Classical properties of interest are the distribution of and correlations within families of periodic orbits. Quantum features in our focus concern spectral fluctuations and energy eigenfunctions in the semiclassical limit where classical periodic orbits strongly influence quantum behavior. More\-over, a semiclassical theory of universal quantum transport through clean chaotic conductors is under construction.

B2

Limits of representations
A. Huckleberry, M Bochum, M. Kus, CTP Warsaw, P. Littelmann, M Köln, G. Marinescu, M Köln, J. Winkelmann, M Bochum
Geometric and representation theorectic phenomena which depend on an integer N which can be interpreted as 1/hbar play the leading role in the project. In particular, relationships between entanglement complexity and orbital symplectic structures are analyzed in contexts of large tensor products. Algorithms which deliver information on weights of representations via polytope geometry have been and will be developed. Asymptotic phenomena connected with large N limits of eigenfunctions and integral kernels which arise in complex geometry are studied. Using the tools of Nevanlinna theory, holomorphic curves in directed systems of group manifolds and sequences of representation spaces will be analyzed with the long range goal of establishing connections between limiting spectral information and the dynamics of associated classical systems.
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