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Quantum Chaos on Graphs
Abstract
We quantize graphs (networks) which consist of a finite number of bonds and nodes. We show that their spectral statistics is well reproduced by random matrix theory. We also define a classical phase space for the graph, where the dynamics is mixing and the periodic orbits (loops on the graph) proliferate exponentially. An exact trace formula for the quantum spectrum is developed and used to investigate the origin of the connection between random matrix theory and the underlying chaotic classical dynamics. Being an exact theory, and due to its relative simplicity, it offers new insights into this problem which is at the forefront of the research in quantum chaos and related fields.
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Citations
Cited by
Kirchhoff's rule for quantum wires
Kostrykin, V, & Schrader, R. (1999) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/32/4/006 · Cited by 431
Quantum graphs: Applications to quantum chaos and universal spectral statistics
Gnutzmann∥, S., & Smilansky, U. (2006) · Advances in Physics · doi:10.1080/00018730600908042 · Cited by 346
Self-citationSmall-World Networks: Evidence for a Crossover Picture
Barthélémy, M., & Amaral, L. A. N. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.3180 · Cited by 306
Graph models for waves in thin structures
Kuchment, P. (2002) · Waves in Random Media · doi:10.1088/0959-7174/12/4/201 · Cited by 288
Decoherence in quantum walks – a review
KENDON, V. (2007) · Mathematical Structures in Computer Science · doi:10.1017/s0960129507006354 · Cited by 252
Metadata
- Authors
- Kottos, T., & Smilansky, U.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1997-12-15
- Volume
- 79
- Issue
- 24
- Pages
- 4794-4797
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2028396877
- Cited by
- 461
- References
- 0
- FWCI
- 9.44
- Type
- journal article
- Language
- en
- Open access
- closed
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- Kottos, T., & Smilansky, U. (1997). Quantum Chaos on Graphs. Physical Review Letters. https://doi.org/10.1103/physrevlett.79.4794
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
