Journal article
Quantum graphs: Applications to quantum chaos and universal spectral statistics
Advances in Physics, Vol.55(6-May), pp.527-625
Jul/2006
Abstract
During the last few years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wavefunction 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. In particular, we summarize 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.
Details
- Title
- Quantum graphs; Applications to quantum chaos and universal spectral statistics
- Creators
- Sven Gnutzmann (null)Uzy Smilansky (null) - 972WIS_INST___89
- Resource Type
- Journal article; Review
- Publication Details
- Advances in Physics, Vol.55(6-May), pp.527-625; Jul/2006
- Number of pages
- 99
- Language
- English
- DOI
- https://doi.org/10.1080/00018730600908042
- Record Identifier
- 993266847503596
Metrics
15 Record Views