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

Abstract

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 that significant improvement in accuracy is obtained for simple chaotic systems where comparison can be made with brute-force diagonalization. The accuracy of the method persists even when the short-time dynamics of the system or ensemble is known only in a classical approximation. Further improvement in the rate of convergence is obtained when the method is combined with the correlation function bootstrapping approach introduced previously.

9 pages, 6 figures

References in corpus (19)

• Statistics of energy levels and eigenfunctions in disordered systems
• Self-consistent multi-mode lasing theory for complex or random lasing media
• Periodic-Orbit Theory of Level Correlations
• Linear and Nonlinear Theory of Eigenfunction Scars
• Approach to ergodicity in quantum wave functions
• Periodic-orbit theory of universal level correlations in quantum chaos
• New Class of Eigenstates in Generic Hamiltonian Systems
• Correlations in Chaotic Eigenfunctions at Large Separation
• Weak Quantum Ergodicity
• Wave Function Structure in Two-Body Random Matrix Ensembles
• Amplitude distribution of eigenfunctions in mixed systems
• Quantum billiards and constrained random wave correlations
• Phase-space correlations of chaotic eigenstates
• Residual Coulomb interaction fluctuations in chaotic systems: the boundary, random plane waves, and semiclassical theory
• A Method to Modify RMT using Short-Time Behavior in Chaotic Systems
• Interaction Matrix Element Fluctuations in Ballistic Quantum Dots: Random Wave Model
• Correlation Function Bootstrapping in Quantum Chaotic Systems
• Semiclassical theory of non-local statistical measures: residual Coulomb interactions
• A trivial observation on time reversal in random matrix theory

Cited by in corpus (4)

• Characterization of random features of chaotic eigenfunctions in unperturbed basis
• Correlations in eigenfunctions of quantum chaotic systems with sparse Hamiltonian matrices
• Correlations between spectra with different symmetry: any chance to be observed?
• Quantum birthmarks: Ergodicity breaking beyond scarring