Reduced Density Matrix Equations for Combined Instantaneous and Delayed Dissipation in Many-Atom Systems, and their Numerical Treatment

Abstract

A many-atom system excited by light or by collisions, such as is found in the photo-excitation of a molecule adsorbed on a surface or in photosynthesis and vision, leads to energy dissipation on different time scales. A fast dissipation typically occurs due to electronic energy relaxation in the medium, while a slow (delayed) dissipation arises from vibrational energy relaxation. In what follows we briey present a reduced density matrix treatment based on a self-consistent coupling of primary and secondary regions which includes their time correlation, in a generalization valid for an active medium. We also describe a numerical procedure based on an extended Runge-Kutta algorithm which can be applied to systems undergoing simultaneous fast and slow rates of dissipation. We illustrate our treatment with a realistic model for an adsorbate on a solid surface, CO=Cu(001) photoexcited by a femtosecond pulse of light and relaxing by electronic and vibrational pathways. Results for the populations of vibronic states versus time show that they oscillate due to vibrational coupling through dissipative interaction with the substrate, and are therefore in coherent quantum states. The total populations of electronic states are however little affected by vibrational motions. The same formalism and numerical procedure can be followed for example in treatments of photoexcitation of chromophores in biomolecular systems.