Berlin 2005 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 2: Hauptvorträge II

MP 2.2: Hauptvortrag

Dienstag, 8. März 2005, 17:25–18:20, TU MA043

Symmetry classes of disordered fermions (the 10-fold way) — •Martin Zirnbauer — Institut für Theoretische Physik, Universität Köln, Zülpicher Str.77, 50937 Köln

Building upon Dyson’s fundamental 1962 article known in random matrix theory as ’the threefold way’ we classify disordered fermion systems with quadratic Hamiltonians by their unitary and antiunitary symmetries. Important examples are afforded by noninteracting quasiparticles in disordered metals and superconductors, and by relativistic fermions in random gauge field backgrounds. The primary data of the classification are a Nambu space of fermionic field operators which carry a representation of some symmetry group. Eliminating the unitary symmetries by transferring to an irreducible block of equivariant homomorphisms, we show that each set of irreducible block data determines an irreducible classical compact symmetric space. Conversely, every irreducible classical compact symmetric space occurs in this way. This proves the correspondence between symmetry classes and symmetric spaces conjectured some time ago.