Non-markovian Quantum Dissipation in the Pre- Sence of External Fields

This article reviews from both theoretical and numerical aspects three non-equivalent complete second-order formulations of quantum dissipation theory, in which both the reduced dynamics and the initial canonical thermal equilibrium are properly treated in the weak system-bath coupling limit. Two of these formulations are rather familiar as the time-local and the memory-kernel prescriptions, while another which can be termed as correlated driving-dissipation equations of motion will be shown to have the combined merits of the two conventional formulations. By exploiting the exact solutions to the driven Brownian oscillator system, we demonstrate that the time-local and correlated driving-dissipation equations of motion formulations are usually better than their memory-kernel counterparts, in terms of their applicability to a broad range of system-bath coupling, nonMarkovian, and temperature parameters. Numerical algorithms are detailed for an efficient evaluation of both the reduced canonical thermal equilibrium state and the non-Markovian evolution at any temperature, in the presence of arbitrary time-dependent external fields. Progress in Theoretical Chemistry and Physics, Vol. 12: Advanced Topics in Theoretical Chemical Physics, edited by J. Maruani, R. Lefebvre, and E. Brändas, pages 7–40. c © 2003 Kluwer Academic Publishers. Printed in the Netherlands.