Reduced density matrix vibrational relaxation

Contributions from terms like Cs pyare smaU and ignored in the summation. Starting from the von Neumann-Liouville equation, a reduced density matrix for the system mode is derived using the time-dependent perturbation theory after tracing over the bath degrees of freedom. The commonly employed Markov approximation is avoided and no assumption of a separation in timescales between system and bath mode relaxation is invoked in this theory [84]. The ultimate result for the evolution of the ground state vibrational population is... 

From a quantum mechanical perspective, the transient vibrational relaxation dynamics is often studied within a reduced density matrix formalism. The dissipative dynamics of the so-called open system is described by a Liouville von Neumann equation that includes implicitly the effects of the surroundings on the dynamics... 

We present in Section 2 the formalism giving the equations for the reduced density operator and for competing instantaneous and delayed dissipation. Section 3 presents matrix equations in a form suitable for numerical work, and the details of the numerical procedure used to solve the integrodiffer-ential equations with the two types of dissipative processes. In Section 4 on applications to adsorbates, results are shown for quantum state populations versus time for the dissipative dynamics of CO/Cu(001). The fast electronic relaxation to the ground electronic state is shown first without the slow relaxation of the frustrated translation mode of CO vibrations, for comparison with previous work, and this is followed by results with both fast and slow relaxation. In Section 5 we comment on the general conclusions that can be reached in problems involving both vibrational and electronic relaxation at surfaces. 

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