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Random-matrix theories in quantum physics: common concepts
Open accessAbstract
We review the development of random-matrix theory (RMT) during the last fifteen years. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new “statistical mechanics”: Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.
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Cites
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Statistical mechanics of complex networks
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Random matrix approach to cross correlations in financial data
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Self-citationDynamics of Loschmidt echoes and fidelity decay
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Black holes and random matrices
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Torquato, S. (2018) · Physics Reports · doi:10.1016/j.physrep.2018.03.001 · Cited by 499
Metadata
- Authors
- Guhr, T., Müller–Groeling, A., & Weidenmüller, H. A.
- Venue
- Physics Reports
- Publisher
- Elsevier BV
- Published
- 1998-06
- Volume
- 299
- Issue
- 4-6
- Pages
- 189-425
- ISSN
- 0370-1573 (ISSN-L)
- OpenAlex
- W1963596092
- Cited by
- 2,211
- References
- 9
- FWCI
- 87.24
- Type
- journal article
- Language
- en
- Open access
- green
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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