Wigner flow reveals topological order in quantum phase space dynamics

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.

6 pages, 6 figures

References in corpus (2)

• Classical to quantum transition of a driven nonlinear nanomechanical resonator
• Quantum dynamics and breakdown of classical realism in nonlinear oscillators

Cited by in corpus (5)

• Equivalence between free quantum particles and those in harmonic potentials and its application to instantaneous changes
• Non-classicality from the phase-space flow analysis of the Weyl-Wigner quantum mechanics
• Wigner's representation of quantum mechanics in integral form and its applications
• Entropy non-conservation and boundary conditions for Hamiltonian dynamical systems
• Topological origin of quantum mechanical vacuum transitions and tunneling