  We report the results of a study of the dynamics of a two-state system
coupled to an environment with peaked spectral density. An exact analytical
expression for the bath correlation function is obtained. Validity range of
various approximations to the correlation function for calculating the
population difference of the system are discussed as function of tunneling
splitting, oscillator frequency, coupling constant, damping rate and the
temperature of the bath. An exact expression for the population difference for
a limited range of parameters, is derived.
