  We use the numerical flow-equation renormalization method to study a
nonlinear bath at low temperatures. The model of our nonlinear bath consists of
a single two-level system coupled to a linear oscillator bath. The effects of
this nonlinear bath are analyzed by coupling it to a spin, whose relaxational
dynamics under the action of the bath is studied by calculating spin-spin
correlation functions. As a first result, we derive flow equations for a
general four-level system coupled to an oscillator bath, valid at low
temperatures. We then treat the two-level system coupled to our nonlinear bath
as a special case of the dissipative four-level system. We compare the effects
of the nonlinear bath with those obtained using an effective linear bath, and
study the differences between the two cases at low temperatures.
