On a non-Markoffian master equation

Fritz Haake

S. Swain

Starting from the multi-level master equation a non-Markoffian rate equation is derived. Explicit expressions for the transition rates between each pair of atomic levels in this equation are derived at it is shown that these may be interpreted as the sum of one-photon, two-photon,..., etc. transition rates connecting the given pair of levels. The non-Markoffian master equation is exact and so can describe long- or short-time behaviour under monochromatic or broad-band excitation. The exact steady-state solutions are obtained by solving a Markoffian rate equation.

V.P. Vstovsky

E. B. Davies

Tomohei Sasada

The non-Markoffian effect on superradiance from an assembly of many harmonic oscillators is investigated based on a theory recently developed by Bonifacio, Schwendimann, and Haake. A superradiance master equation is solved exactly by introducing the coherent state basis. It is show how the retardation effect, which takes into account a dynamical role of the photon field played during the radiating processes, modifies the shape and Poissonian statistics of superradiant pulses obtained from the Markoffian approach.

Hanno Gassmann, Florian Marquardt, Christoph Bruder

We analyze a model of a nonlinear bath consisting of a single two-level system coupled to a linear bath (a classical noise force in the limit considered here). This allows us to study the effects of a nonlinear, non-Markoffian bath in a particularly simple situation. We analyze the effects of this bath onto the dynamics of a spin by calculating the decay of the equilibrium correlator of the z-component of the spin. The exact results are compared with those obtained using three commonly used approximations: a Markoffian master equation for the spin dynamics, a weak-coupling approximation, and the substitution of a linear bath for the original nonlinear bath.