You need JavaScript to view this

Trace formulae for arithmetical systems

Technical Report:

Abstract

For quantum problems on the pseudo-sphere generated by arithmetic groups there exist special trace formulae, called trace formulae for Hecke operators, which permit the reconstruction of wave functions from the knowledge of periodic orbits. After a short discussion of this subject, the Hecke operators trace formulae are presented for the Dirichlet problem on the modular billiard, which is a prototype of arithmetical systems. The results of numerical computations for these semiclassical type relations are in good agreement with the directly computed eigenfunctions. (author) 23 refs.; 2 figs.
Publication Date:
Sep 01, 1992
Product Type:
Technical Report
Report Number:
IPNO-TH-92-78
Reference Number:
SCA: 661100; PA: AIX-25:003897; EDB-94:015532; ERA-19:005490; NTS-94:014767; SN: 93001120973
Resource Relation:
Other Information: PBD: Sep 1992
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIRICHLET PROBLEM; SEMICLASSICAL APPROXIMATION; EIGENFUNCTIONS; ERGODIC HYPOTHESIS; GROUP THEORY; ORBITS; QUANTUM MECHANICS; QUANTUM OPERATORS; WAVE FUNCTIONS; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10109785
Research Organizations:
Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire
Country of Origin:
France
Language:
English
Other Identifying Numbers:
Other: ON: DE94609570; TRN: FR9303103003897
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
FRN
Size:
14 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Bogomolny, E B, Georgeot, B, Giannoni, M J, and Schmit, C. Trace formulae for arithmetical systems. France: N. p., 1992. Web.
Bogomolny, E B, Georgeot, B, Giannoni, M J, & Schmit, C. Trace formulae for arithmetical systems. France.
Bogomolny, E B, Georgeot, B, Giannoni, M J, and Schmit, C. 1992. "Trace formulae for arithmetical systems." France.
@misc{etde_10109785,
title = {Trace formulae for arithmetical systems}
author = {Bogomolny, E B, Georgeot, B, Giannoni, M J, and Schmit, C}
abstractNote = {For quantum problems on the pseudo-sphere generated by arithmetic groups there exist special trace formulae, called trace formulae for Hecke operators, which permit the reconstruction of wave functions from the knowledge of periodic orbits. After a short discussion of this subject, the Hecke operators trace formulae are presented for the Dirichlet problem on the modular billiard, which is a prototype of arithmetical systems. The results of numerical computations for these semiclassical type relations are in good agreement with the directly computed eigenfunctions. (author) 23 refs.; 2 figs.}
place = {France}
year = {1992}
month = {Sep}
}