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.
Bohigas, O;
Ullmo, D;
[1]
Tomsovic, S
[2]
- Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire
- Washington Univ., Seattle, WA (United States). Dept. of Physics
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}
}
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}
}