The Semiclassical Regime of the Chaotic Quantum-Classical Transition
  An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one dimensional chaotic dynamical systems. Environmental fluctuations -- characteristic of all realistic dynamical systems -- suppress the development of fine structure in classical phase space and damp nonlocal contributions to the semiclassical Wigner function which would otherwise invalidate the approximation. This dual regularization of the singular nature of the semiclassical limit is demonstrated by a numerical investigation of the chaotic Duffing oscillator. 
Benjamin D. Greenbaum, Salman Habib, Kosuke Shizume and Bala Sundaram