Regensburg 2000 – scientific programme

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DY: Dynamik und Statistische Physik

DY 25: Symposium Niveaustatistik und Quantenchaos

DY 25.7: Fachvortrag

Tuesday, March 28, 2000, 17:10–17:30, H3

Quantum chaos on Graphs - recent developments and new results — •Gregor Tanner — School of Mathematical Sciences, University of Nottingham, University Park, UK–Nottingham NG7 2RD

Quantum graphs have recently been introduced as model systems to study quantum problems with chaotic classical limit. The most fascinating features of quantum graphs can be constructed easily and almost at will covering all kinds of classical limits such as chaotic dynamics, scattering or diffusive behaviour. Yet, the quantum mechanics is easy to control and and quantum graphs show the same phenomena as observed in more general quantum systems such as universality in spectral statistics or Anderson localisation.

I will review recent developments and generalise the concepts of quantum graphs to arbitrary, directed graphs with unitary transfer matrices. The form factor can be written in terms of correlated periodic orbit pair contributions which converge towards the random matrix limit with increasing number of vertices in the graph.