Correlations between periodic orbits and their rôle in spectral statistics

MMA Sieber, K Richter

Research output: Contribution to journalArticle (Academic Journal)peer-review

140 Citations (Scopus)

Abstract

We consider off-diagonal contributions to double sums over periodic orbits that arise in semiclassical approximations for spectral statistics of classically chaotic quantum systems. We identify pairs of periodic orbits whose actions are strongly correlated. For a class of systems with uniformly hyperbolic dynamics, we demonstrate that these pairs of orbits give rise to a r2 contribution to the spectral form factor K(r) which agrees with random matrix theory. Most interestingly, this contribution has its origin in a next-to-leading-order behavior of a classical distribution function for long times. 05.45.Mt,03.65.Sq
Translated title of the contributionCorrelations between periodic orbits and their rôle in spectral statistics
Original languageEnglish
Pages (from-to)128 - 133
Number of pages6
JournalPhysica Scripta
VolumeT90
DOIs
Publication statusPublished - Mar 2001

Bibliographical note

Publisher: Institute of Physics Publishing
Other identifier: IDS Number 427XQ
Other: Info:Quantum Chaos Y2K: the 116th Nobel Symposium, 13-17 June 2000, B\uOOE4\ckasog Castle, Sweden

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