You need JavaScript to view this

Manifestations of classical phase space structures in quantum mechanics

Technical Report:

Abstract

Using two coupled quartic oscillators for illustration, the quantum mechanics of simple systems whose classical analogues have varying degrees of non-integrability is investigated. By taking advantage of discrete symmetries and dynamical quasidegeneracies it is shown that Percival`s semiclassical classification scheme, i.e. eigenstates may be separated into a regular or an irregular group, basically works. Some observations of intermediate status states are made. Generalized ensembles are constructed which apply equally well to both spectral and eigenstate properties. They typically show non-universal, but nevertheless characteristic level fluctuations. In addition, they predict `semiclassical localization` of eigenfunctions and `quantum suppression of chaos` which are quantitatively borne out in the quantum systems. (author) 101 refs.; 27 figs.; 6 tabs.
Authors:
Bohigas, O; Ullmo, D; [1]  Tomsovic, S [2] 
  1. Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire
  2. Washington Univ., Seattle, WA (United States). Dept. of Physics
Publication Date:
Nov 01, 1992
Product Type:
Technical Report
Report Number:
IPNO-TH-92-92
Reference Number:
SCA: 661100; PA: AIX-25:003898; EDB-94:015533; ERA-19:005491; NTS-94:014768; SN: 93001120974
Resource Relation:
Other Information: DN: Submitted to Physics Reports (NL).; PBD: Nov 1992
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QUANTUM MECHANICS; PHASE SPACE; SEMICLASSICAL APPROXIMATION; EIGENSTATES; FLUCTUATIONS; OSCILLATORS; SYMMETRY; 661100; CLASSICAL AND QUANTUM MECHANICS
OSTI ID:
10109790
Research Organizations:
Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire
Country of Origin:
France
Language:
English
Other Identifying Numbers:
Other: ON: DE94609571; TRN: FR9303109003898
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
FRN
Size:
162 p.
Announcement Date:
Jun 30, 2005

Technical Report:

Citation Formats

Bohigas, O, Ullmo, D, and Tomsovic, S. Manifestations of classical phase space structures in quantum mechanics. France: N. p., 1992. Web.
Bohigas, O, Ullmo, D, & Tomsovic, S. Manifestations of classical phase space structures in quantum mechanics. France.
Bohigas, O, Ullmo, D, and Tomsovic, S. 1992. "Manifestations of classical phase space structures in quantum mechanics." France.
@misc{etde_10109790,
title = {Manifestations of classical phase space structures in quantum mechanics}
author = {Bohigas, O, Ullmo, D, and Tomsovic, S}
abstractNote = {Using two coupled quartic oscillators for illustration, the quantum mechanics of simple systems whose classical analogues have varying degrees of non-integrability is investigated. By taking advantage of discrete symmetries and dynamical quasidegeneracies it is shown that Percival`s semiclassical classification scheme, i.e. eigenstates may be separated into a regular or an irregular group, basically works. Some observations of intermediate status states are made. Generalized ensembles are constructed which apply equally well to both spectral and eigenstate properties. They typically show non-universal, but nevertheless characteristic level fluctuations. In addition, they predict `semiclassical localization` of eigenfunctions and `quantum suppression of chaos` which are quantitatively borne out in the quantum systems. (author) 101 refs.; 27 figs.; 6 tabs.}
place = {France}
year = {1992}
month = {Nov}
}