Tunneling in a Lorenz-like model for an active wave-particle entity

TL;DR

This paper models a wave-particle entity using a Lorenz-like system to explore quantum tunneling analogs, revealing how velocity fluctuations and chaos influence barrier crossing and transmission probabilities.

Contribution

It introduces a simplified Lorenz-based model to study tunneling phenomena in active wave-particle entities, linking non-equilibrium dynamics to tunneling-like behavior.

Findings

Velocity fluctuations induce sensitivity and unpredictability in barrier crossing.

Transmission probability varies smoothly with system parameters.

Wave-like features appear in transmitted and reflected probability densities.

Abstract

Active wave-particle entities (WPEs) emerge as self-propelled oil droplets on the free surface of a vibrating oil bath. The particle (droplet) periodically imprints decaying waves on the liquid surface which in turn guide the particle motion, resulting in a two-way coupling between the particle and its self-generated waves. Such WPEs have been shown to exhibit hydrodynamic analogs of various quantum features. In this work, we theoretically and numerically explore a dynamical analog of tunneling by considering a simple setup of a one-dimensional WPE incident on an isolated Gaussian potential barrier. Our idealized model takes the form of a perturbed Lorenz system which we use to explore the dynamics and statistics of barrier crossing as a function of initial conditions and system parameters. Our work highlights that velocity fluctuations of the WPE at high memories that are rooted in non-equilibrium features of the Lorenz system, such as spiraling motion towards equilibrium points and transient chaos, give rise to - (i) sensitivity and unpredictability in barrier crossing, (ii) smooth variations in transmission probability as a function of system parameters, and (iii) wave-like features in the transmitted and reflected probability density profiles.