- The quantum kicked rotator is linearly coupled to a heat bath via its momentum coordinate. A momentum-space formulation of the Feynman-Vernon formalism is introduced to find the reduced propagator. The Wigner picture of the dynamics is adopted. It is found that it is a good approximation to ignore the ``friction'' effect and to replace the bath by a correlated noise source. For certain values of the friction coefficient, this replacement is exact. Destruction of coherence at zero temperature is qualitatively different for an undriven rotator.