Quantum

Metric and Dispersive Dynamics of Phase Perturbations in Bohmian Quantum Mechanics

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 19/10/2026, 04:13:24 UTC.

Briefings

A new study in arXiv:2610.22737v1 derives an effective metric for phase perturbations in Bohmian quantum mechanics by linearizing hydrodynamic equations via the Madelung transformation. The authors demonstrate that a previously obtained metric is a specific case of a broader framework where the complete functional variation of the quantum potential is retained, allowing external classical potentials to be included. This generalization introduces dispersive corrections and sources in the effective Klein-Gordon equation, with the local geometry separated from these corrections. The study identifies conditions where these additional terms become negligible, recovering homogeneous propagation for Gaussian wave packets of free particles.

Key points

• The study derives an effective metric for phase perturbations in Bohmian quantum mechanics using linearized hydrodynamic equations.
• The authors show that a previously obtained metric is a particular case of a more general structure involving the complete functional variation of the quantum potential.

Context

This research addresses the mathematical structure of phase perturbations in Bohmian dynamics, specifically by linearizing hydrodynamic equations associated with the Madelung transformation. It provides a framework where the quantum potential's complete functional variation is retained, enabling the incorporation of external classical potentials and generating dispersive corrections in the effective Klein-Gordon equation.

Limitations

The evidence is limited to a single arXiv preprint (arXiv:2610.22737v1) published in October 2026. The findings are preliminary and subject to peer review; the authors explicitly state that the additional terms may become negligible under specific conditions, but the exact thresholds for this recovery are not fully detailed in the provided text.

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