Quantum Liouville-space trajectories for dissipative systems

In this paper we present a new quantum-trajectory based treatment of quantum dynamics suitable for dissipative systems. Starting from a de Broglie/Bohm-like representation of the quantum density matrix, we derive and define quantum equations-of-motion for Liouville-space trajectories for a generalized system coupled to a dissipative environment. Our theory includes a vector potential which mixes forward and backwards propagating components and non-local quantum potential which continuously produces coherences in the system. These trajectories are then used to propagate an adaptive Lagrangian grid which carries the density matrix, $\rho(x,y)$, and the action, $A(x,y)$, thereby providing a complete hydrodynamic-like description of the dynamics.