Classical mechanics from quantum state diffusion - a phase-space approach

Quantum state diffusion (QSD) provides a natural unravelling of a mixed-state open quantum system into component pure states. We investigate the semiclassical limit of QSD in a phase-space approach using the Wigner function. As (h) over bar --> 0, QSD exhibits two very different dynamical regimes, depending on the volume of phase space covered by the quantum state. For large volumes there is a localization regime represented by classical nonlinear and nonlocal diffusion processes. For small volumes, comparable in size with a Planck cell, there is a wavepacket regime. Here, the centroid of the wavepacket follows a classical Langevin equation, obtained through the adiabatic elimination of the dynamics of the second-order moments of the wavepacket. The corresponding Fokker-Planck equation is identical to the one obtained from the classical limit of the original mixed-state dynamics. In the companion paper we present an axiomatic approach to a classical theory of quantum localization without using the underlying QSD theory.