Localization in the quantum-kicked-rotator problem leads to nontrivial dynamical correlations that are absent in the classical limit. Consequently, both coherence and diffusion in the presence of colored noise depend on its long-range autocorrelations. This implies that a Markovian treatment of the dynamics for a system that is coupled to a low-temperature heat bath is not valid even if the system is classically chaotic.

• Received 27 November 1990

DOI:https://doi.org/10.1103/PhysRevLett.67.1945