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Statistical Theory of the Energy Levels of Complex Systems. II
Abstract
The distribution function of spacings S between nearest neighbors, in a long series of energy levels with average spacing D, is studied. The statistical properties of S are defined in terms of an ensemble of systems described in a previous paper. For large values of t = (πS/2D), it is shown that the distribution of S can be deduced from the thermodynamical properties of a certain model. The model, which replaces the eigenvalue distribution by a continuous fluid, can be studied by the methods of classical electrostatics, potential theory, and thermodynamics. In this way the distribution function of spacings S is found to be asymptotically Q(t)=At17/8 exp[−14t2−12t]for large t. The numerical constant A can in principle not be determined from such a continuum model. Reasons are given for considering the remaining factors in the formula for Q(t) to be reliable.
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Citations
Cited by
Random-matrix theory of quantum transport
Beenakker, C. W. J. (1997) · Reviews of Modern Physics · doi:10.1103/revmodphys.69.731 · Cited by 2,551
Nonperturbative two-dimensional quantum gravity
Gross, D. J., & Migdal, A. A. (1990) · Physical Review Letters · doi:10.1103/physrevlett.64.127 · Cited by 1,013
Quantum integrable systems related to lie algebras
Olshanetsky, M. A., & Perelomov, A. M. (1983) · Physics Reports · doi:10.1016/0370-1573(83)90018-2 · Cited by 991
Wigner, E. P. (1967) · SIAM Review · doi:10.1137/1009001 · Cited by 532
The spectrum edge of random matrix ensembles
Forrester, P. J. (1993) · Nuclear Physics B · doi:10.1016/0550-3213(93)90126-a · Cited by 517
Metadata
- Authors
- Dyson, F. J.
- Venue
- Journal of Mathematical Physics
- Publisher
- AIP Publishing
- Published
- 1962-01-01
- Volume
- 3
- Issue
- 1
- Pages
- 157-165
- ISSN
- 0022-2488 (ISSN-L)
- 1089-7658
- OpenAlex
- W4243445458
- Cited by
- 498
- References
- 0
- FWCI
- 9.79
- Type
- journal article
- Language
- en
- Open access
- closed
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