Quantum Graphology

Details Quantum Graphology Quantum Graphology

2005-06-24

arxiv.org/abs/nlin/0506051v1

Nonlinear Sciences

Chaotic Dynamics

15 pages, 7 figures, Paper presented at the 2nd Workshop on Quantum Chaos and Localisation Phenomenon, May 20th, 2005, Warsaw,

Scientific paper

We review quantum chaos on graphs. We construct a unitary operator which represents the quantum evolution on the graph and study its spectral and wavefunction statistics. This operator is the analogue of the classical evolution operator on the graph. It allow us to establish a connection between the corresponding periodic orbits and the statistical properties of eigenvalues and eigenfunctions. Specifically, for the energy-averaged spectral form factor we derived an exact combinatorial expression which illustrate the role of correlations between families of isometric orbits. We also show that enhanced wave function localization due to the presence of short unstable periodic orbits and strong scarring can rely on completely different mechanisms.

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