Lund, 22nd - 24th January 2004
Quantum Ergodicity - Basic Ideas and Recent Developments
Jon Harrison

Quantum spectral properties of graphs with spin

Jon Harrison (Berlin)

We compare the quantisations of compact mixing graphs with the Dirac and Schrödinger operators. Terms in a diagramatic expansion of the spectral form factors are related by averages over the group of spin transformations. In random matrix theory the power series expansions of the COE and CSE form factors are closely related. The same relation is derived for quantum graphs with time-reversal symmetry provided the spin transformations on the graph quantised with the Dirac operator generate an irreducible quaternionic representation.
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