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| 1. | R Ramaswamy, Augustin S; Rabitz, H Stochastic theory of intramolecular energy transfer Journal Article The Journal of Chemical Physics, 69 (12), pp. 5509-5517, 1978, ISSN: 0021-9606. Abstract | Links | BibTeX | Tags: energy conservation, probability, Stochasticity @article{Ramaswamy1978, title = {Stochastic theory of intramolecular energy transfer}, author = {R Ramaswamy, S Augustin and H Rabitz}, url = {https://doi.org/10.1063/1.436544}, doi = {10.1063/1.436544}, issn = {0021-9606}, year = {1978}, date = {1978-12-15}, journal = {The Journal of Chemical Physics}, volume = {69}, number = {12}, pages = {5509-5517}, abstract = {The problem of internal energy redistribution in an isolated polyatomic molecule is treated by a stochastic theory approach. The fundamental assumption of this work is that a random phase approximation is valid at specific time intervals. This results in the replacement of the Schrödinger equation by a master equation that governs the evolution of a probability distribution in the quantum levels of the molecule. No assumptions regarding the strength of the coupling are made, and the problem of energy conservation is specifically considered. A stochastic variable is introduced in order to satisfy the requirement that the total energy remain fixed. The further approximation of the master equation by a Fokker–Planck diffusion-like equation is outlined; the latter approach is particularly attractive for treating large molecules. Finally, the master‐equation theory is applied to a model problem representing a linearly constrained triatomic molecule, and the time evolution of an initially localized excitation is discussed.}, keywords = {energy conservation, probability, Stochasticity}, pubstate = {published}, tppubtype = {article} } The problem of internal energy redistribution in an isolated polyatomic molecule is treated by a stochastic theory approach. The fundamental assumption of this work is that a random phase approximation is valid at specific time intervals. This results in the replacement of the Schrödinger equation by a master equation that governs the evolution of a probability distribution in the quantum levels of the molecule. No assumptions regarding the strength of the coupling are made, and the problem of energy conservation is specifically considered. A stochastic variable is introduced in order to satisfy the requirement that the total energy remain fixed. The further approximation of the master equation by a Fokker–Planck diffusion-like equation is outlined; the latter approach is particularly attractive for treating large molecules. Finally, the master‐equation theory is applied to a model problem representing a linearly constrained triatomic molecule, and the time evolution of an initially localized excitation is discussed. |