On the Born and Markov Approximations: Phonon Relaxation and Coherent Excitation of Adsorbed Molecules.

The phonon relaxation of the vibrational adbond of an adsorbed molecule and a phonon-damped adbond irradiated by a laser are studied. Approximations are made within the Zwanzig projection operator formalism in order to arrive at a master equation for the reduced density operator of a small subsystem (the adbond) in contact with a reservoir (the phonons). The conditions of validity for the Born and Markov approximations are derived. It is shown that the master equation is only valid for times t tau sub c, where tau sub c is the characteristic time of the reservoir. These results are then applied to the phonon relaxation of the vibrational adbond of physisorbed molecules. It is shown that for Carbon Monoxide adsorbed on Nickel or Copper (a strongly-bound physisorbed system), the Born and Markov approximations are not justified. For the weakly-bound system Arogon on Tungesten numerical results show that these approximations can be made. Finally, an adbond interacting with both laser radiation and lattice vibrations is considered. This system can be regarded as a subsystem (the adbond) in contact with two reservoirs, where the conditions for validity of the Markov approximation is then seen to be more severe than when each reservoir is considered independently. For the phonons, these conditions can never be matched. However, for an initial state given by an adbond in equilibrium with the lattice vibrations, the conditions for validity of the approximation prove to be the same as for the phonons and the laser considered independently.