Phase space bottlenecks

A comparison of quantum and classical intramolecular dynamics for collinear OCS

Lester L. Gibson, George C Schatz, Mark A Ratner, Michael J. Davis

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

We compare quantum and classical mechanics for a collinear model of OCS at an energy (20 000 cm-1) where Davis [J. Chem. Phys. 83, 1016 ( 1985)] had previously found that phase space bottlenecks associated with golden mean tori inhibit classical flow between different chaotic regions in phase space. Accurate quantum eigenfunctions for this two mode system are found by diagonalizing a large basis of complex Gaussian functions, and these are then used to study the evolution of wave packets which have 20 000 cm-1 average energies. By examining phase space (Husimi) distributions associated with the wave functions, we conclude that these golden mean tori do indeed act as bottlenecks which constrain the wave packets to evolve within one (or a combination of) regions. The golden mean tori do not completely determine the boundaries between regions, however. Bottlenecks associated with resonance trapping and with separatrix formation are also involved. The analysis of the Husimi distributions also indicates that each exact eigenstate is nearly always associated with just one region, and because of this, superpositions of eigenstates that are localized within a region remain localized in that region at all times. This last result differs from the classical picture at this energy where flow across the bottlenecks occurs with a 2-4 ps lifetime. Since the classical phase space area through which flux must pass to cross the bottlenecks is small compared to ℏ for OCS, the observed difference between quantum and classical dynamics is not surprising. Examination of the time development of normal mode energies indicates little or no energy flow quantum mechanically for wave packet initial conditions. Classical trajectory bundles constructed from the wave packet phase space distributions also show little or no energy flow even though noticeable flow is observed for more localized bundles chosen from the turnstile associated with flow through the bottleneck.

Original languageEnglish
Pages (from-to)3263-3272
Number of pages10
JournalJournal of Chemical Physics
Volume86
Issue number6
Publication statusPublished - 1987

Fingerprint

Wave packets
wave packets
eigenvectors
bundles
energy
Wave functions
Eigenvalues and eigenfunctions
Mechanics
classical mechanics
Trajectories
Fluxes
quantum mechanics
examination
trapping
trajectories
wave functions
life (durability)

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Phase space bottlenecks : A comparison of quantum and classical intramolecular dynamics for collinear OCS. / Gibson, Lester L.; Schatz, George C; Ratner, Mark A; Davis, Michael J.

In: Journal of Chemical Physics, Vol. 86, No. 6, 1987, p. 3263-3272.

Research output: Contribution to journalArticle

@article{99e119737c7143c9b38dc944e1692b57,
title = "Phase space bottlenecks: A comparison of quantum and classical intramolecular dynamics for collinear OCS",
abstract = "We compare quantum and classical mechanics for a collinear model of OCS at an energy (20 000 cm-1) where Davis [J. Chem. Phys. 83, 1016 ( 1985)] had previously found that phase space bottlenecks associated with golden mean tori inhibit classical flow between different chaotic regions in phase space. Accurate quantum eigenfunctions for this two mode system are found by diagonalizing a large basis of complex Gaussian functions, and these are then used to study the evolution of wave packets which have 20 000 cm-1 average energies. By examining phase space (Husimi) distributions associated with the wave functions, we conclude that these golden mean tori do indeed act as bottlenecks which constrain the wave packets to evolve within one (or a combination of) regions. The golden mean tori do not completely determine the boundaries between regions, however. Bottlenecks associated with resonance trapping and with separatrix formation are also involved. The analysis of the Husimi distributions also indicates that each exact eigenstate is nearly always associated with just one region, and because of this, superpositions of eigenstates that are localized within a region remain localized in that region at all times. This last result differs from the classical picture at this energy where flow across the bottlenecks occurs with a 2-4 ps lifetime. Since the classical phase space area through which flux must pass to cross the bottlenecks is small compared to ℏ for OCS, the observed difference between quantum and classical dynamics is not surprising. Examination of the time development of normal mode energies indicates little or no energy flow quantum mechanically for wave packet initial conditions. Classical trajectory bundles constructed from the wave packet phase space distributions also show little or no energy flow even though noticeable flow is observed for more localized bundles chosen from the turnstile associated with flow through the bottleneck.",
author = "Gibson, {Lester L.} and Schatz, {George C} and Ratner, {Mark A} and Davis, {Michael J.}",
year = "1987",
language = "English",
volume = "86",
pages = "3263--3272",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
publisher = "American Institute of Physics Publising LLC",
number = "6",

}

TY - JOUR

T1 - Phase space bottlenecks

T2 - A comparison of quantum and classical intramolecular dynamics for collinear OCS

AU - Gibson, Lester L.

AU - Schatz, George C

AU - Ratner, Mark A

AU - Davis, Michael J.

PY - 1987

Y1 - 1987

N2 - We compare quantum and classical mechanics for a collinear model of OCS at an energy (20 000 cm-1) where Davis [J. Chem. Phys. 83, 1016 ( 1985)] had previously found that phase space bottlenecks associated with golden mean tori inhibit classical flow between different chaotic regions in phase space. Accurate quantum eigenfunctions for this two mode system are found by diagonalizing a large basis of complex Gaussian functions, and these are then used to study the evolution of wave packets which have 20 000 cm-1 average energies. By examining phase space (Husimi) distributions associated with the wave functions, we conclude that these golden mean tori do indeed act as bottlenecks which constrain the wave packets to evolve within one (or a combination of) regions. The golden mean tori do not completely determine the boundaries between regions, however. Bottlenecks associated with resonance trapping and with separatrix formation are also involved. The analysis of the Husimi distributions also indicates that each exact eigenstate is nearly always associated with just one region, and because of this, superpositions of eigenstates that are localized within a region remain localized in that region at all times. This last result differs from the classical picture at this energy where flow across the bottlenecks occurs with a 2-4 ps lifetime. Since the classical phase space area through which flux must pass to cross the bottlenecks is small compared to ℏ for OCS, the observed difference between quantum and classical dynamics is not surprising. Examination of the time development of normal mode energies indicates little or no energy flow quantum mechanically for wave packet initial conditions. Classical trajectory bundles constructed from the wave packet phase space distributions also show little or no energy flow even though noticeable flow is observed for more localized bundles chosen from the turnstile associated with flow through the bottleneck.

AB - We compare quantum and classical mechanics for a collinear model of OCS at an energy (20 000 cm-1) where Davis [J. Chem. Phys. 83, 1016 ( 1985)] had previously found that phase space bottlenecks associated with golden mean tori inhibit classical flow between different chaotic regions in phase space. Accurate quantum eigenfunctions for this two mode system are found by diagonalizing a large basis of complex Gaussian functions, and these are then used to study the evolution of wave packets which have 20 000 cm-1 average energies. By examining phase space (Husimi) distributions associated with the wave functions, we conclude that these golden mean tori do indeed act as bottlenecks which constrain the wave packets to evolve within one (or a combination of) regions. The golden mean tori do not completely determine the boundaries between regions, however. Bottlenecks associated with resonance trapping and with separatrix formation are also involved. The analysis of the Husimi distributions also indicates that each exact eigenstate is nearly always associated with just one region, and because of this, superpositions of eigenstates that are localized within a region remain localized in that region at all times. This last result differs from the classical picture at this energy where flow across the bottlenecks occurs with a 2-4 ps lifetime. Since the classical phase space area through which flux must pass to cross the bottlenecks is small compared to ℏ for OCS, the observed difference between quantum and classical dynamics is not surprising. Examination of the time development of normal mode energies indicates little or no energy flow quantum mechanically for wave packet initial conditions. Classical trajectory bundles constructed from the wave packet phase space distributions also show little or no energy flow even though noticeable flow is observed for more localized bundles chosen from the turnstile associated with flow through the bottleneck.

UR - http://www.scopus.com/inward/record.url?scp=3943058021&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3943058021&partnerID=8YFLogxK

M3 - Article

VL - 86

SP - 3263

EP - 3272

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 6

ER -