A Method to Modify RMT using Short-Time Behavior in Chaotic Systems

Details A Method to Modify RMT using Short-Time Behavior in Chaotic Systems A Method to Modify RMT using Short-Time Behavior in Chaotic Systems

2009-07-29

arxiv.org/abs/0907.5037v1

Phys. Rev. E 80, 035205(R) (2009)

Nonlinear Sciences

Chaotic Dynamics

5 pages, 3 figures

Scientific paper

10.1103/PhysRevE.80.035205

We discuss a modification to Random Matrix Theory eigenstate statistics, that systematically takes into account the non-universal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian, instead requiring only a knowledge of short-time dynamics for a chaotic system or ensemble of similar systems. Standard Random Matrix Theory and semiclassical predictions are recovered in the limits of zero Ehrenfest time and infinite Heisenberg time, respectively. As examples, we discuss wave function autocorrelations and cross-correlations, and show how the approach leads to a significant improvement in accuracy for simple chaotic systems where comparison can be made with brute-force diagonalization.

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