Quantum dephasing and decay of classical correlation functions in chaotic systems

We discuss the dephasing induced by the internal classical chaotic motion in the absence of any external environment. To this end we consider a suitable extension of fidelity for mixed states which is measurable in a Ramsey interferometry experiment. We then relate the dephasing to the decay of this quantity which, in the semiclassical limit, is expressed in terms of an appropriate classical correlation function. Our results are derived analytically for the example of a nonlinear driven oscillator and then numerically confirmed for the kicked rotor model.