### Abstract

The role of non-markovian effects in the stochastic treatment of vibrational- translational energy transfer in collinear atom—diatom collisions is examined. A comparison of transition probabilities using both markovian and nonmarkovian types of master equations, as well as exact time dependent quantum mechanics, is made for various values of the system parameters m and a. We find that for certain ranges of the system parameters, the deviations between markovian and non-markovian theories are substantial. Only in the perturbation theory limit and in the limit of low m/α^{2} values and high enough initial translational energies such that an impulsive approximation for translational motion is accurate are the markovian and non-markovian results similar. An analysis of the collision dynamics indicates that the markovian and non-markovian probabilities agree with each other and with the exact probabilities when action-angle correlations are weak while none of these theories agree (except by accident) when such effects are strong.

Original language | English |
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Pages (from-to) | 257-272 |

Number of pages | 16 |

Journal | Molecular Physics |

Volume | 38 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1979 |

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### ASJC Scopus subject areas

- Biophysics
- Molecular Biology
- Physical and Theoretical Chemistry
- Condensed Matter Physics

### Cite this

**Stochastic theory of vibrational energy transfer in collinear atom-diatom collisions : The role of non-markovian effects.** / King, Frederick W.; Schatz, George C.

Research output: Contribution to journal › Article

*Molecular Physics*, vol. 38, no. 1, pp. 257-272. https://doi.org/10.1080/00268977900101641

}

TY - JOUR

T1 - Stochastic theory of vibrational energy transfer in collinear atom-diatom collisions

T2 - The role of non-markovian effects

AU - King, Frederick W.

AU - Schatz, George C

PY - 1979

Y1 - 1979

N2 - The role of non-markovian effects in the stochastic treatment of vibrational- translational energy transfer in collinear atom—diatom collisions is examined. A comparison of transition probabilities using both markovian and nonmarkovian types of master equations, as well as exact time dependent quantum mechanics, is made for various values of the system parameters m and a. We find that for certain ranges of the system parameters, the deviations between markovian and non-markovian theories are substantial. Only in the perturbation theory limit and in the limit of low m/α2 values and high enough initial translational energies such that an impulsive approximation for translational motion is accurate are the markovian and non-markovian results similar. An analysis of the collision dynamics indicates that the markovian and non-markovian probabilities agree with each other and with the exact probabilities when action-angle correlations are weak while none of these theories agree (except by accident) when such effects are strong.

AB - The role of non-markovian effects in the stochastic treatment of vibrational- translational energy transfer in collinear atom—diatom collisions is examined. A comparison of transition probabilities using both markovian and nonmarkovian types of master equations, as well as exact time dependent quantum mechanics, is made for various values of the system parameters m and a. We find that for certain ranges of the system parameters, the deviations between markovian and non-markovian theories are substantial. Only in the perturbation theory limit and in the limit of low m/α2 values and high enough initial translational energies such that an impulsive approximation for translational motion is accurate are the markovian and non-markovian results similar. An analysis of the collision dynamics indicates that the markovian and non-markovian probabilities agree with each other and with the exact probabilities when action-angle correlations are weak while none of these theories agree (except by accident) when such effects are strong.

UR - http://www.scopus.com/inward/record.url?scp=84913337183&partnerID=8YFLogxK

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U2 - 10.1080/00268977900101641

DO - 10.1080/00268977900101641

M3 - Article

VL - 38

SP - 257

EP - 272

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 1

ER -