Statistical properties of many-particle spectra. III. Ergodic behavior in random-matrix ensembles

Journal Article · Tue May 01 04:00:00 EDT 1979 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(79)90254-9· OSTI ID:6045308

Pandey, A

The ergodic problem is defined for random-matrix ensembles and some conditions for ergodicity given. Ergodic properties are demonstrated for the orthogonal, unitary and symplectic cases of the Gaussian and circular ensembles, and also for the Poisson ensemble. The one-point measures, viz., the eigenvalue density, the number statistic and the k'th-nearest-neighbor spacings are shown to be ergodic and the ensemble variances of the corresponding spectral averages are explicity calculated. It is moreover shown, by using Dyson's cluster functions, that all the k-point correlation functions are themselves ergodic as are therefore the fluctuation measures which follow from them. It is proved also that the local fluctuation properties of the Gaussian ensembles are stationary over the spectrum.

• Research Organization: Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627
• OSTI ID: 6045308
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 119:1; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CORRELATION FUNCTIONS
ENERGY LEVELS
ENERGY SPECTRA
ENERGY-LEVEL DENSITY
ERGODIC HYPOTHESIS
FLUCTUATIONS
FUNCTIONS
GAUSS FUNCTION
GAUSSIAN PROCESSES
HYPOTHESIS
MANY-BODY PROBLEM
SPECTRA
SPECTRAL DENSITY
SPECTRAL FUNCTIONS
VARIATIONS