Self-consistent perturbation theory for random matrix ensembles
- 7 May 1990
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 23 (9) , 1555-1565
- https://doi.org/10.1088/0305-4470/23/9/018
Abstract
An arbitrary but known random matrix ensemble is subjected to a perturbation by any of the three classical random matrix ensembles (GOE, GUE and GSE). Using a BBGKY hierarchy for the correlation functions of the eigenvalues, they propose a self-consistent perturbation expansion and give the result for the two-point function to lowest order in integral form. By way of illustration, the integral is solved for the special case of a Poisson ensemble perturbed by any of the classical ensembles, thereby recovering a result previously derived by other methods.Keywords
This publication has 6 references indexed in Scilit:
- Statistical theory of precompound reactions: The multistep compound processAnnals of Physics, 1986
- Grassmann integration in stochastic quantum physics: The case of compound-nucleus scatteringPhysics Reports, 1985
- Fluctuations of quantum spectra and their semiclassical limit in the transition between order and chaosJournal of Physics A: General Physics, 1985
- Semiclassical level spacings when regular and chaotic orbits coexistJournal of Physics A: General Physics, 1984
- A Brownian-Motion Model for the Eigenvalues of a Random MatrixJournal of Mathematical Physics, 1962
- "Repulsion of Energy Levels" in Complex Atomic SpectraPhysical Review B, 1960