Integrating Random Matrix Theory Predictions with Short-Time Dynamical Effects in Chaotic Systems

摘要

We discuss a modification to Random Matrix Theory eigenstate statistics, thatsystematically takes into account the non-universal short-time behavior ofchaotic systems. The method avoids diagonalization of the Hamiltonian, insteadrequiring only a knowledge of short-time dynamics for a chaotic system orensemble of similar systems. Standard Random Matrix Theory and semiclassicalpredictions are recovered in the limits of zero Ehrenfest time and infiniteHeisenberg time, respectively. As examples, we discuss wave functionautocorrelations and cross-correlations, and show that significant improvementin accuracy is obtained for simple chaotic systems where comparison can be madewith brute-force diagonalization. The accuracy of the method persists even whenthe short-time dynamics of the system or ensemble is known only in a classicalapproximation. Further improvement in the rate of convergence is obtained whenthe method is combined with the correlation function bootstrapping approachintroduced previously.