  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 spin's z-component. 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.
