On stochastic reductions in molecular collision theory: Projection operator formalism; application to classical and quantum forced oscillator model

George C Schatz, Frank J. McLafferty, John Ross

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

A method is developed for treating complex molecular collision processes through the application of stochastic reduction formalisms. We begin by describing a projection operator method for decomposing a complicated collision system into two (or more) subsystems, each of which is assumed to be weakly correlated (not necessarily weakly interacting) with the others. Approximations to this correlation are then introduced, and this results in a set of coupled equations for the reduced density operators (or classical phase space distributions) associated with each subsystem. We then examine the classical mechanical application of this theory to the forced oscillator model of V-T energy transfer. Arguments of multiple time scales are used to uncouple the stochastically reduced equations of motion, and thus we may evaluate the memory kernel analytically. This leads to a single diffusion equation for the time evolution of the action in the oscillator during the collision. Comparison with the corresponding exact results indicates excellent agreement of low order moments of the classical distributions of action in the limit of small energy transfer (i.e., ΔE/ℏω

Original languageEnglish
Pages (from-to)3609-3623
Number of pages15
JournalJournal of Chemical Physics
Volume66
Issue number8
Publication statusPublished - 1977

Fingerprint

molecular collisions
Energy transfer
projection
energy transfer
oscillators
formalism
operators
collisions
Equations of motion
equations of motion
moments
Data storage equipment
approximation

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

On stochastic reductions in molecular collision theory : Projection operator formalism; application to classical and quantum forced oscillator model. / Schatz, George C; McLafferty, Frank J.; Ross, John.

In: Journal of Chemical Physics, Vol. 66, No. 8, 1977, p. 3609-3623.

Research output: Contribution to journalArticle

@article{442b1ec1f1514e448ee9e21190f98eb8,
title = "On stochastic reductions in molecular collision theory: Projection operator formalism; application to classical and quantum forced oscillator model",
abstract = "A method is developed for treating complex molecular collision processes through the application of stochastic reduction formalisms. We begin by describing a projection operator method for decomposing a complicated collision system into two (or more) subsystems, each of which is assumed to be weakly correlated (not necessarily weakly interacting) with the others. Approximations to this correlation are then introduced, and this results in a set of coupled equations for the reduced density operators (or classical phase space distributions) associated with each subsystem. We then examine the classical mechanical application of this theory to the forced oscillator model of V-T energy transfer. Arguments of multiple time scales are used to uncouple the stochastically reduced equations of motion, and thus we may evaluate the memory kernel analytically. This leads to a single diffusion equation for the time evolution of the action in the oscillator during the collision. Comparison with the corresponding exact results indicates excellent agreement of low order moments of the classical distributions of action in the limit of small energy transfer (i.e., ΔE/ℏω",
author = "Schatz, {George C} and McLafferty, {Frank J.} and John Ross",
year = "1977",
language = "English",
volume = "66",
pages = "3609--3623",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
publisher = "American Institute of Physics Publising LLC",
number = "8",

}

TY - JOUR

T1 - On stochastic reductions in molecular collision theory

T2 - Projection operator formalism; application to classical and quantum forced oscillator model

AU - Schatz, George C

AU - McLafferty, Frank J.

AU - Ross, John

PY - 1977

Y1 - 1977

N2 - A method is developed for treating complex molecular collision processes through the application of stochastic reduction formalisms. We begin by describing a projection operator method for decomposing a complicated collision system into two (or more) subsystems, each of which is assumed to be weakly correlated (not necessarily weakly interacting) with the others. Approximations to this correlation are then introduced, and this results in a set of coupled equations for the reduced density operators (or classical phase space distributions) associated with each subsystem. We then examine the classical mechanical application of this theory to the forced oscillator model of V-T energy transfer. Arguments of multiple time scales are used to uncouple the stochastically reduced equations of motion, and thus we may evaluate the memory kernel analytically. This leads to a single diffusion equation for the time evolution of the action in the oscillator during the collision. Comparison with the corresponding exact results indicates excellent agreement of low order moments of the classical distributions of action in the limit of small energy transfer (i.e., ΔE/ℏω

AB - A method is developed for treating complex molecular collision processes through the application of stochastic reduction formalisms. We begin by describing a projection operator method for decomposing a complicated collision system into two (or more) subsystems, each of which is assumed to be weakly correlated (not necessarily weakly interacting) with the others. Approximations to this correlation are then introduced, and this results in a set of coupled equations for the reduced density operators (or classical phase space distributions) associated with each subsystem. We then examine the classical mechanical application of this theory to the forced oscillator model of V-T energy transfer. Arguments of multiple time scales are used to uncouple the stochastically reduced equations of motion, and thus we may evaluate the memory kernel analytically. This leads to a single diffusion equation for the time evolution of the action in the oscillator during the collision. Comparison with the corresponding exact results indicates excellent agreement of low order moments of the classical distributions of action in the limit of small energy transfer (i.e., ΔE/ℏω

UR - http://www.scopus.com/inward/record.url?scp=36749104942&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749104942&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:36749104942

VL - 66

SP - 3609

EP - 3623

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

ER -