On the derivation of rate equations for collisionless molecular multiphoton processes

Abstract

Starting with the complete molecular Liouville equation and making use of the Mori–Zwanzig projection operator formalism we derive generalized rate equations which describe the collisionless dynamics of level populations in the quasicontinuum of molecular multiphoton processes. We define precisely the complete molecular information required for the description of these processes which is expressed in the form of a hierarchy of intramolecular dipole correlation functions. We then discuss the general conditions under which the equations attain the form of simple rate equations and show how the complete molecular information reduces considerably in this case to three relevant quantities per transition: an integrated Rabi frequency, a dephasing time and ratios of statistical weights of the levels.