Stochastic theory of intramolecular energy transfer

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 diffusionlike 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.