Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
Abstract
During the last years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wave function statistics. In the first part of this review we give a detailed introduction to the spectral theory of quantum graphs and discuss exact trace formulae for the spectrum and the quantum-to-classical correspondence. The second part of this review is devoted to the spectral statistics of quantum graphs as an application to quantum chaos. Especially, we summarise recent developments on the spectral statistics of generic large quantum graphs based on two approaches: the periodic-orbit approach and the supersymmetry approach. The latter provides a condition and a proof for universal spectral statistics as predicted by random-matrix theory.
Cite
@article{arxiv.nlin/0605028,
title = {Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics},
author = {Sven Gnutzmann and Uzy Smilansky},
journal= {arXiv preprint arXiv:nlin/0605028},
year = {2012}
}
Comments
Review article, published version, special thanks to Steve Fulling who found some errors in the first manuscript before publication