Correlations between periodic orbits and their rôle in spectral statistics

MMA Sieber; K Richter

doi:10.1238/PHYsica.Topical.090a00128

Correlations between periodic orbits and their rôle in spectral statistics

MMA Sieber, K Richter

Research output: Contribution to journal › Article (Academic Journal) › peer-review

180 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 contribution	Correlations between periodic orbits and their rôle in spectral statistics
Original language	English
Pages (from-to)	128 - 133
Number of pages	6
Journal	Physica Scripta
Volume	T90
DOIs	https://doi.org/10.1238/PHYsica.Topical.090a00128
Publication status	Published - 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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10.1238/PHYsica.Topical.090a00128

http://www.iop.org/EJ/abstract/1402-4896/2001/T90/018/

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title = "Correlations between periodic orbits and their r{\^o}le in spectral statistics",

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",

author = "MMA Sieber and K Richter",

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",

year = "2001",

month = mar,

doi = "10.1238/PHYsica.Topical.090a00128",

language = "English",

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pages = "128 -- 133",

journal = "Physica Scripta",

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TY - JOUR

T1 - Correlations between periodic orbits and their rôle in spectral statistics

AU - Sieber, MMA

AU - Richter, K

N1 - 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

PY - 2001/3

Y1 - 2001/3

N2 - 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

AB - 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

U2 - 10.1238/PHYsica.Topical.090a00128

DO - 10.1238/PHYsica.Topical.090a00128

M3 - Article (Academic Journal)

SN - 1281-1847

VL - T90

SP - 128

EP - 133

JO - Physica Scripta

JF - Physica Scripta

ER -

Correlations between periodic orbits and their rôle in spectral statistics

Abstract

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