We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the Glauber $Q$ or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical drift and quantum diffusion in contractive and expansive directions. By this mechanism the system follows a “quantum smoothened” approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows.

• Received 11 October 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.073601