Stabilization of Quantum Energy Flows within the Approximate Quantum Trajectory Approach

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The hydrodynamic, or the de Broglie-Bohm, formulation provides an alternative to the conventional time-dependent Schrödinger equation based on quantum trajectories. The trajectory dynamics scales favorably with the system size, but it is, generally, unstable due to singularities in the exact quantum potential. The approximate quantum potential based on the fitting of the nonclassical component of the momentum operator in terms of a small basis is numerically stable but can lead to inaccurate large net forces in bound systems. We propose to compensate errors in the approximate quantum potential by applying a semiempirical friction-like force. This significantly improves the description of zero-point energy in bound systems. Examples are given for one-dimensional models relevant to nuclear dynamics.