Bonn 2001 – scientific programme

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MP: Theoretische und Mathematische Grundlagen der Physik

MP IV: HV IV

MP IV.1: Invited Talk

Tuesday, March 27, 2001, 15:00–16:00, HS VIII

The Tenfold Way: Symmetry Classification of Disordered Single-Particle Systems — •Martin Zirnbauer — Institut für Theoretische Physik, Universität Köln

Dyson, in his “threefold way” [J. Math. Phys. 3 (1963) 1198], proved that the most general kind of matrix ensemble (for quantum mechanical systems with some fixed but arbitrary symmetry group) reduces to a direct product of irreducible ensembles each of which belongs to one of three known types. In this talk I describe a minimal extension of Dyson’s notion of irreducible matrix ensemble, to include ensembles that appear in systems of noninteracting fermions such as the quasiparticles of a disordered superconductor. Given this extension, I show that there exists a one-to-one correspondence between irreducible matrix ensembles and the ten large families of symmetric spaces.