Anharmonic quantum mechanical systems do not feature phase space trajectories

TL;DR

This paper demonstrates that anharmonic quantum systems lack trajectory-based phase space dynamics due to quantum coherences causing singularities, challenging classical analogies and impacting numerical methods in quantum phase space analysis.

Contribution

It provides a general proof that quantum phase space distributions with negative values cannot support trajectories, revealing the fundamental difference from classical mechanics.

Findings

Quantum coherences cause singularities in phase space velocity fields.

Anharmonic quantum systems do not have trajectory-based phase space dynamics.

This explains numerical difficulties in quantum phase space studies.

Abstract

Phase space dynamics in classical mechanics is described by transport along trajectories. Anharmonic quantum mechanical systems do not allow for a trajectory-based description of their phase space dynamics. This invalidates some approaches to quantum phase space studies. We first demonstrate the absenceof trajectories in general terms. We then give an explicit proof for all quantum phase space distributions with negative values: we show that the generation of coherences in anharmonic quantum mechanical systems is responsible for the occurrence of singularities in their phase space velocity fields, and vice versa. This explains numerical problems repeatedly reported in the literature, and provides deeper insight into the nature of quantum phase space dynamics.