Energy gap dependence of vibrational dephasing rates in a bath: A semigroup description

The quantum dynamical semigroup formalism provides an appealing general framework for discussing factors that affect pure vibrational dephasing rates in chemical systems. Within this framework, we formulate a Poisson model of pure vibrational dephasing which is more generally applicable than the commonly employed stochastic Gaussian dephasing model. In the limit of small and frequent phase changes, the Poisson model reduces to the stochastic Gaussian form. We find that for certain vibrational states of the lithium dimer in argon, the stochastic Gaussian model is valid, while for other states large and abrupt phase changes clearly require application of the Poisson model. In the former case, dephasing rates increase with the difference in quantum number between constituent vibrational states, while in the latter case, the dependence on quantum number difference or energy gap can become negligible. Recent experimental advances described by Amitay and Leone are expected to permit experimental tests of our theoretical predictions.