Evolution of Quantum Phase Space Distribution: a Trajectory-Density Approach

The trajectory-density method of a quantum system is developed by using local Koopman and Frobenius-Perron operators. We propose a new scheme of approximation from two sets of trajectory-density mixed equations. By examining the local generation and termination of trajectories, we show how they can be adopted to the propagation of negative values of the Wigner function even if it starts off positive everywhere.