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Quantum Liouville-space trajectories for dissipative systems

Jeremy B. Maddox·Eric R. Bittner
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Abstract

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, $ρ(x,y)$, and the action, $A(x,y)$, thereby providing a complete hydrodynamic-like description of the dynamics.

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Jeremy B. Maddox, Eric R. Bittner. 2001-02-09. Quantum Liouville-space trajectories for dissipative systems. https://arxiv.org/abs/quant-ph/0102055

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