The DOI matches its Crossref record; 89 of the 89 references it cites were found in a registry or an index.
Quantum graphs: Applications to quantum chaos and universal spectral statistics
Open accessAbstract
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.
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Cites
Chaos in Classical and Quantum Mechanics
Gutzwiller, M. C. (1990) · Interdisciplinary Applied Mathematics · doi:10.1007/978-1-4612-0983-6 · Cited by 3,914
Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws
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Metadata
- Authors
- Gnutzmann∥, S., & Smilansky, U.
- Venue
- Advances in Physics
- Publisher
- Informa UK Limited
- Published
- 2006-07
- Volume
- 55
- Issue
- 5-6
- Pages
- 527-625
- ISSN
- 0001-8732 (ISSN-L)
- 1460-6976
- OpenAlex
- W2163018374
- Cited by
- 346
- References
- 89
- FWCI
- 10.01
- Type
- journal article
- Language
- en
- Open access
- green
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