Nature of matrix elements in the quantum chaotic domain of interacting particle systems
Abstract
Description
There is a newly emerging understanding that in the chaotic domain of isolated finite interacting many particle systems smoothed densities define the statistical description of these systems and these densities follow from embedded (two-body) random matrix ensembles and their various deformations. These ensembles predict that the smoothed form of matrix elements of a transition operator between the chaotic eigenstates weighted by the densities at the two ends (i.e. the bivariate strength density) will be a bivariate Gaussian with the bivariate correlation coefficient arising out of the non-commutability of the hamiltonian and the transition operator involved. The ensemble theory extends to systems with a mean-field and a chaos generating two-body interaction (as in nuclei, atoms and diffusive quantum dots). These developments in many-body quantum chaos are described with special reference to one-body transition operators.
10 pages, Latex file, two figures (3 eps-files), talk delivered by V.K.B. Kota at the National Conference on Dynamical Systems: Recent Developments', November 4-6, 1999, Unversity of Hyderabad, Hyderabad, India
10 pages, Latex file, two figures (3 eps-files), talk delivered by V.K.B. Kota at the National Conference on Dynamical Systems: Recent Developments', November 4-6, 1999, Unversity of Hyderabad, Hyderabad, India