Self-energy fields solutions to the generalized reduced Liouville equationin the perturbative approach

A direct approach for the generalized reduced Liouville equation of motion decoupling problem associated with open quantum systems within the superope rator formalism is presented. The procedure is based on inversion of the pe rturbation series for the energy representation of the density operator so as to obtain one for the proper self-energy fields that emerge as a consequ ence of the analytic character of the associated spectral representation. T hus, the perturbation series that arises from the iteration of the energy-d ependent matrix elements hierarchy involved in the statistical operator all ows, upon further expansion of the inverse of such series, to get formally exact expressions for the corrections to all orders of the self-energy fiel ds. The lower order corrections of these fields are discussed in terms of r esonant and nonresonant contributions, The present approach provides matrix equations that show the close relation between the environment effects rep resented by the self-energy fields and the relaxation kernel that drives th e system-reservoir interaction. (C) 2000 John Wiley & Sons, Inc.