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Chemical Physics

A generalized langevin equation for wave functions. Intramolecular vibrational dephasing as a stochastic process

Kiyohiko Someda, Raphael David Levine

Published Jun 1, 1994• 10 citations
Publisher
DOI
10.1016/0301-0104(94)00075-1

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The dephasing of a high-frequency intramolecular vibrational mode in a molecular crystal is successively investigated by the cumulant perturbation expansion method as in the preceding papers in this series, I and II. The dephasing of the high-frequency mode is brought on by the thermal excitation of a low-frequency mode in the same molecule as in I and II. In this paper, however, the intramolecular vibrational modes are expressed by the bands of the exciton waves traveling through the crystal (in I and II, the intramolecular vibrational modes are expressed by the localized excitation in one molecule). The calculation shows that the spectrum becomes considerably broad as the temperature increases, while the narrowing is observed as the band widths of the exciton waves increases.
The quantum-mechanical formulation of a class of stochastic optimal control problems is investigated and two versions of non-linear Schrödinger equation are derived. First, a wave-function is introduced which connects the probability density function of a diffusion process with the minimum cost functional of the stochastic optimal control problem associated with the diffusion process. It is then demonstrated that this wave-function satisfies a kind of Schrödinger-Langevin equation in quantum physics. Finally, the probabilistic interpretation of the wave-function is discussed.