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Quantum maps from transfer operators

Technical Report:

Abstract

The Selberg zeta function {zeta}{sub S}(s) yields an exact relationship between the periodic orbits of a fully chaotic Hamiltonian system (the geodesic flow on surfaces of constant negative curvature) and the corresponding quantum system (the spectrum of the Laplace-Beltrami operator on the same manifold). It was found that for certain manifolds, {zeta}{sub S}(s) can be exactly rewritten as the Fredholm-Grothendieck determinant det(1-T{sub s}), where T{sub s} is a generalization of the Ruelle-Perron-Frobenius transfer operator. An alternative derivation of this result is given, yielding a method to find not only the spectrum but also the eigenfunctions of the Laplace-Beltrami operator in terms of eigenfunctions of T{sub s}. Various properties of the transfer operator are investigated both analytically and numerically for several systems. (author) 30 refs.; 16 figs.; 2 tabs.
Publication Date:
Sep 01, 1992
Product Type:
Technical Report
Report Number:
IPNO-TH-92-74
Reference Number:
SCA: 661100; PA: AIX-25:003895; EDB-94:015530; ERA-19:005488; NTS-94:014765; SN: 93001120971
Resource Relation:
Other Information: DN: Submitted to Physica. D (NL).; PBD: Sep 1992
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QUANTUM OPERATORS; MATHEMATICAL MANIFOLDS; EIGENFUNCTIONS; EIGENVALUES; GEODESICS; HAMILTONIAN FUNCTION; ORBITS; QUANTUM MECHANICS; TOPOLOGICAL MAPPING; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10109776
Research Organizations:
Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire
Country of Origin:
France
Language:
English
Other Identifying Numbers:
Other: ON: DE94609568; TRN: FR9303100003895
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
FRN
Size:
60 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Bogomolny, E B, and Carioli, M. Quantum maps from transfer operators. France: N. p., 1992. Web.
Bogomolny, E B, & Carioli, M. Quantum maps from transfer operators. France.
Bogomolny, E B, and Carioli, M. 1992. "Quantum maps from transfer operators." France.
@misc{etde_10109776,
title = {Quantum maps from transfer operators}
author = {Bogomolny, E B, and Carioli, M}
abstractNote = {The Selberg zeta function {zeta}{sub S}(s) yields an exact relationship between the periodic orbits of a fully chaotic Hamiltonian system (the geodesic flow on surfaces of constant negative curvature) and the corresponding quantum system (the spectrum of the Laplace-Beltrami operator on the same manifold). It was found that for certain manifolds, {zeta}{sub S}(s) can be exactly rewritten as the Fredholm-Grothendieck determinant det(1-T{sub s}), where T{sub s} is a generalization of the Ruelle-Perron-Frobenius transfer operator. An alternative derivation of this result is given, yielding a method to find not only the spectrum but also the eigenfunctions of the Laplace-Beltrami operator in terms of eigenfunctions of T{sub s}. Various properties of the transfer operator are investigated both analytically and numerically for several systems. (author) 30 refs.; 16 figs.; 2 tabs.}
place = {France}
year = {1992}
month = {Sep}
}