Universität zu Köln

Huynh, H. M. and Kunze, M. (2015). Partner orbits and action differences on compact factors of the hyperbolic plane. I: Sieber-Richter pairs. Nonlinearity, 28 (3). S. 593 - 624. BRISTOL: IOP PUBLISHING LTD. ISSN 1361-6544

Full text not available from this repository.

Abstract

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. In this paper we consider the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. We prove the existence of a periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space which is a '2-encounter'; such configurations are called 'Sieber-Richter pairs' in physics literature. Furthermore, we derive an estimate for the action difference of the partners. In the second part of this paper (Huynh, submitted), an inductive argument is provided to deal with higher-order encounters.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Huynh, H. M. UNSPECIFIED UNSPECIFIED UNSPECIFIED Kunze, M. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-406178
DOI:	10.1088/0951-7715/28/3/593
Journal or Publication Title:	Nonlinearity
Volume:	28
Number:	3
Page Range:	S. 593 - 624
Date:	2015
Publisher:	IOP PUBLISHING LTD
Place of Publication:	BRISTOL
ISSN:	1361-6544
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SPECTRAL FORM-FACTOR; PERIODIC-ORBITS; QUANTUM CHAOS; UNIVERSALITY Multiple languages Mathematics, Applied; Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/40617