Fractional motions of an active particle on the quantum vortex

TL;DR

This paper analytically explores the diffusive behavior of active particles influenced by quantum vortices on superfluid helium, considering viscoelastic effects, vortex forces, thermal noise, and confinement.

Contribution

It provides new analytical solutions for the particle dynamics under complex forces and memory effects, advancing understanding of quantum vortex-driven motion.

Findings

Derived analytical solutions for particle probability densities in different regimes.

Characterized the influence of viscoelastic memory and vortex forces on particle diffusion.

Analyzed the effects of confinement on active particle dynamics.

Abstract

We analytically investigate the diffusive motion inferred from experimental observations of active particles driven by quantum vortices on the surface of superfluid helium. We first study the dynamical behavior of an active particle subject to a viscoelastic memory effect characterized by a power-law kernel. We then analyze the dynamics of an active particle under a uniform vortex force, thermal noise, and viscous dissipation subject to a power-law kernel. Next, by including a harmonic confining force, we obtain analytical solutions for the joint probability density in two distinct time regimes.