### 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 language | English |
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Pages (from-to) | 3609-3623 |

Number of pages | 15 |

Journal | Journal of Chemical Physics |

Volume | 66 |

Issue number | 8 |

Publication status | Published - 1977 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

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## Cite this

*Journal of Chemical Physics*,

*66*(8), 3609-3623.