Wigner flow reveals topological order in quantum phase space dynamics

TL;DR

This paper introduces a quantum phase space flow that uncovers hidden topological order and complex dynamics in quantum systems, bridging classical phase portraits and quantum behavior.

Contribution

It defines a quantum analog of classical phase space flow, revealing topological order and complex structures in quantum dynamics previously unnoticed.

Findings

Reveals hidden topological order in quantum phase space

Identifies quantum flow as an analog to classical trajectories

Shows complex quantum dynamics constrained by flow winding numbers

Abstract

The behaviour of classical mechanical systems is characterised by their phase portraits, the collections of their trajectories. Heisenberg's uncertainty principle precludes the existence of sharply defined trajectories, which is why traditionally only the time evolution of wave functions is studied in quantum dynamics. These studies are quite insensitive to the underlying structure of quantum phase space dynamics. We identify the flow that is the quantum analog of classical particle flow along phase portrait lines. It reveals hidden features of quantum dynamics and extra complexity. Being constrained by conserved flow winding numbers, it also reveals fundamental topological order in quantum dynamics that has so far gone unnoticed.