Density Matrix Treatment of the Nonmarkovian Dissipative Dynamics of Adsorbates on Metal Surfaces

Abstract

A density matrix treatment is presented for the vibrational relaxation of the frustrated translational mode of a molecule adsorbed on a metal surface. The system is modeled as a vibrating adsorbate oscillator coupled to a bath of harmonic oscillators representing either phonons or electronic density fluctuations. The integrodifferential equations for time evolution of the density matrix including a (nonmarkovian) delayed dissipation are solved using a generalized Runge-Kutta scheme. The equations are also solved in the instantaneous dissipation and the Markov limits, to ascertain their validity. Numerical results are presented for Na/Cu, CO/Cu, and CO/Pt systems. The population of an initially excited state is given over time for varying temperatures and shows that memory effects are needed in a proper description valid even at short times. Calculations of populations for different coupling strengths between the adsorbate species and the substrate metal surface indicate that a weaker coupling leads to increased oscillation amplitudes and longer relaxation times. The time evolution of quantum coherence is also described.