Correlation Hole of Survival Probability and Level Statistics

Abstract

The relationship between level statistics and the correlation hole inthe survival probability function in generic chaotic systems isinvestigated. It is shown that the depth and the area of the holemeasure the long- and short-range correlations of levels, respectively. Two models of level statistics, namely the Gaudin modeland an independent superposition of circular unitary ensembles, areanalyzed as examples for systems intermediate between chaos andintegrability.