Anharmonic quantum mechanical systems do not feature phase space trajectories. (English) Zbl 1514.82119
Summary: 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 absence of 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.
MSC:
| 82C10 | Quantum dynamics and nonequilibrium statistical mechanics (general) |
| 70K05 | Phase plane analysis, limit cycles for nonlinear problems in mechanics |
| 81Q80 | Special quantum systems, such as solvable systems |
Software:
QuTiPReferences:
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