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Anharmonic quantum mechanical systems do not feature phase space trajectories

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  • Oliva, Maxime
  • Kakofengitis, Dimitris
  • Steuernagel, Ole

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 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.

Suggested Citation

  • Oliva, Maxime & Kakofengitis, Dimitris & Steuernagel, Ole, 2018. "Anharmonic quantum mechanical systems do not feature phase space trajectories," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 201-210.
    • Handle: RePEc:eee:phsmap:v:502:y:2018:i:c:p:201-210
    DOI: 10.1016/j.physa.2017.10.047
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    1. Wojciech Hubert Zurek, 2001. "Sub-Planck structure in phase space and its relevance for quantum decoherence," Nature, Nature, vol. 412(6848), pages 712-717, August.
    2. Sels, Dries & Brosens, Fons & Magnus, Wim, 2012. "Classical trajectories: A powerful tool for solving tunneling problems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 78-81.
    3. Sels, Dries & Brosens, Fons & Magnus, Wim, 2013. "Wigner distribution functions for complex dynamical systems: A path integral approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 326-335.
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