2010/06/29 by A. Matthew Smith, Lev Kaplan, L. Kaplan
Mathematics · Physics and Astronomy · #Applied mathematics #Bootstrapping (finance) #Chaotic #Computer science #Correlation function (quantum field theory) #Eigenvalues and eigenvectors #Mathematics #Matrix (chemical analysis) #Physics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Random matrix #Scientific Research and Discoveries #Semiclassical physics #Spectral density #Standard map #Statistical physics #Statistics #Theoretical and Computational Physics #nlin.CD #quant-ph
paper · pdf · doi:10.1103/physreve.82.016214
published as Phys. Rev. E 82, 016214 (2010) · 9 pages, 6 figures
arxiv created 2010/06/29 · openalex publication_date 2010/07/23 · arxiv updated 2010/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss a modification to random matrix theory eigenstate statistics that systematically takes into account the nonuniversal short-time behavior of chaotic systems. The method avoids diagonalization of the Hamiltonian; instead it requires only 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.