Energy relaxation of a dissipative quantum oscillator

Abstract

The dissipative harmonic oscillator is studied as a model for vibrational relaxation in a liquid environment. Continuum limit expressions are derived for the time-dependent average energy, average width of the population, and the vibrational population itself. The effect of the magnitude of the solute-solvent interaction, expressed in terms of a friction coefficient, solvent temperature, and initial energy of the oscillator on the relaxation has been studied. These results shed light on the recent femtosecond stimulated Raman scattering probe of the 1570 cm(-1) -C=C- stretching mode of trans-Stilbene in the first (S1) excited electronic state. When the oscillator is initially cold with respect to the bath temperature, its average energy and width increase in time. When it is initially hot, the average energy and width decrease with time in qualitative agreement with the experimental observations.

Femtosecond Stimulated Raman Spectroscopy

“…Other examples of isomerization reactions investigated so far include stilbene, 1,1′‐diethyl‐2,2′‐pyridocyanine, 4‐nitro‐4′‐dimethylamino‐azobenzene, vitamin E, azobenzene, and acetylbenzaldehyde . Trans‐stilbene has also been used as a model compound to study solvent‐induced vibrational cooling and heating dynamics …”

Effect of anharmonicity on energy relaxation of a dissipative quantum oscillator

“…Tatchen et al, 24 indicates that theoretical understanding of isomerization of trans-stilbene will be incomplete without the incorporation of the effect of anharmonicity. In the present work, we extended the result by Kumar et al, 7 by including anharmonicity and further used it to shed light on the results of FSRS experiment.…”

“…Kumar et al, used the following Hamiltonian to describe the energy relaxation process in excited state. 7…”

“…In modeling of the environment, harmonic bath model have gained a lot of popularity in deriving numerical as well as analytical results. [7][8][9][10] To circumvent the first bottleneck, one uses some prototype molecules. Similar to vision process, a lot of biologically important processes involve cis-trans isomerization.…”

“…Kumar et al, used the Hamiltonian based Langevin model to study the energy relaxation of harmonic oscillator. 7 They derived the analytical expression for time-dependent average energy as well as energy fluctuations in continuum limit. They also derived the analytical expression for the population spectrum.…”