Spectral density, memory function, and mean relaxation time for resonant subsystem-reservoir interactions

We show that the projection operators P usually employed to derive the Naka jima-Zwanzig master equation are non-Hermitian. As a consequence the operat or QLQ which governs the dynamics of subsystem-reservoir interactions (here Q = 1-P and L is the Liouville operator) is also non-Hermitian and possess es a complex temperature-dependent spectrum of resonances. We use the self- consistent Born approximation to derive a formula for the spectral density of QLQ. From this spectral density we calculate the memory function and mea n relaxation time of subsystem-reservoir correlations. These formulas are c ompared with numerical results obtained from the spin-spin-bath model to te st their accuracy. The memory function and mean relaxation time are essenti al ingredients for the SRA (statistical resonance approximation) theory of microscopic dissipation and decoherence. We show that the SRA master equati on preserves positivity when the memory function derived in this paper is e mployed. (C) 2001 American Institute of Physics.