Phenomenological modeling dissipative systems

In the present phenomenological model, only regions that have not yet equilibrated (i.e., of size s > s t)) can release stress energy in the form of a net amount of heat to the surroundings. This means that only transitions with AF < 0 contribute to the overall relaxation toward equihbrium. Therefore, the rate of energy dissipated by the system can be written as... 

If the system under consideration possesses non-adiabatic electronic couplings within the excited-state vibronic manifold, the latter approach no longer is applicable. Recently, we have developed a simple model which allows for the explicit calculation of RF s for electronically nonadiabatic systems coupled to a heat bath [2]. The model is based on a phenomenological dissipation ansatz which describes the major bath-induced relaxation processes excited-state population decay, optical dephasing, and vibrational relaxation. The model has been applied for the calculation of the time and frequency gated spontaneous emission spectra for model nonadiabatic electron-transfer systems. The predictions of the model have been tested against more accurate calculations performed within the Redfield formalism [2]. It is natural, therefore, to extend this... 

In principle, the theory of nonlinear spectroscopy with femtosecond laser pulses is well developed. A comprehensive and up-to-date exposition of nonlinear optical spectroscopy in the femtosecond time domain is provided by the monograph of Mukamel. ° For additional reviews, see Refs. 7 and 11-14. While many theoretical papers have dealt with the analysis or prediction of femtosecond time-resolved spectra, very few of these studies have explicitly addressed the dynamics associated with conical intersections. In the majority of theoretical studies, the description of the chemical dynamics is based on rather simple models of the system that couples to the laser fields, usually a few-level system or a set of harmonic oscillators. In the case of condensed-phase spectroscopy, dissipation is additionally introduced by coupling the system to a thermal bath, either at a phenomenological level or in a more microscopic maimer via reduced density-matrix theory. 

Collisional relaxation as a dissipation channel was introduced as follows. In light of our hard-cord CS2 model, we have utilized a phenomenological approach toward orientational relaxation based upon thermal buffeting of the molecules. We calculate the mean free time between collisions based upon thermal buffeting of the molecules and using a system of molecular dimensions, temperature and density as specified earlier. This results in a collision frequency of ps per... 

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