Particles and Fields in Superfluids: Insights from the Two-dimensional Gross-Pitaevskii Equation

TL;DR

This study uses detailed numerical simulations to explore how active particles interact with superfluid fields in 2D Gross-Pitaevskii systems, revealing complex dynamics including vortex emission, turbulence, and particle-vortex interactions.

Contribution

It provides new insights into the dynamics of active particles in superfluids, especially how particle mass and configuration influence vortex interactions and turbulence.

Findings

Particle motion varies with mass and external force, showing periodic or chaotic behavior.

Interactions between particles and vortices lead to complex, often turbulent, spatiotemporal patterns.

Configurations of particles and vortices significantly affect the evolution of the superfluid system.

Abstract

We carry out extensive direct numerical simulations (DNSs) to investigate the interaction of active particles and fields in the two-dimensional (2D) Gross-Pitaevskii (GP) superfluid, in both simple and turbulent flows. The particles are active in the sense that they affect the superfluid even as they are affected by it. We tune the mass of the particles, which is an important control parameter. At the one-particle level, we show how light, neutral, and heavy particles move in the superfluid, when a constant external force acts on them; in particular, beyond a critical velocity, at which a vortex-antivortex pair is emitted, particle motion can be periodic or chaotic. We demonstrate that the interaction of a particle with vortices leads to dynamics that depends sensitively on the particle characteristics. We also demonstrate that assemblies of particles and vortices can have rich, and often turbulent spatiotemporal evolution. In particular, we consider the dynamics of the following illustrative initial configurations: (a) one particle placed in front of a translating vortex-antivortex pair; (b) two particles placed in front of a translating vortex-antivortex pair; (c) a single particle moving in the presence of counter-rotating vortex clusters; and (d) four particles in the presence of counter-rotating vortex clusters. We compare our work with earlier studies and examine its implications for recent experimental studies in superfluid Helium and Bose-Einstein condensates.