Interaction of Regular and Chaotic States

Details Interaction of Regular and Chaotic States Interaction of Regular and Chaotic States

2006-11-03

arxiv.org/abs/nucl-th/0611009v1

AnnalsPhys.322:2446-2468,2007

Physics

Nuclear Physics

Nuclear Theory

26 pages, 9 figures

Scientific paper

10.1016/j.aop.2006.11.010

Modelling the chaotic states in terms of the Gaussian Orthogonal Ensemble of random matrices (GOE), we investigate the interaction of the GOE with regular bound states. The eigenvalues of the latter may or may not be embedded in the GOE spectrum. We derive a generalized form of the Pastur equation for the average Green's function. We use that equation to study the average and the variance of the shift of the regular states, their spreading width, and the deformation of the GOE spectrum non-perturbatively. We compare our results with various perturbative approaches.

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