Anomalous transport of a classical wave-particle entity in a tilted potential

TL;DR

This paper models a classical wave-particle system in a tilted potential, revealing anomalous transport behaviors like negative mobility, and suggests experimental exploration of these phenomena in hydrodynamic droplet systems.

Contribution

It introduces a theoretical model transforming the wave-particle dynamics into a Lorenz-like system, uncovering novel anomalous transport regimes not previously characterized.

Findings

Observation of absolute negative mobility (ANM)

Identification of differential negative mobility (DNM)

Detection of lock-in regions with force-independent mobility

Abstract

A classical wave-particle entity in the form of a millimetric walking droplet can emerge on the free surface of a vertically vibrating liquid bath. Such wave-particle entities have been shown to exhibit hydrodynamic analogs of quantum systems. Using an idealized theoretical model of this wave-particle entity in a tilted potential, we explore its transport behavior. The integro-differential equation of motion governing the dynamics of the wave-particle entity transforms to a Lorenz-like system of ordinary differential equations (ODEs) that drives the particle's velocity. Several anomalous transport regimes such as absolute negative mobility (ANM), differential negative mobility (DNM) and lock-in regions corresponding to force-independent mobility, are observed. These observations motivate experiments in the hydrodynamic walking-droplet system for the experimental realizations of anomalous transport phenomena.