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

Area of Science:

• Fluid dynamics
• Nonlinear dynamics
• Hydrodynamic quantum analogs

Background:

• Active wave-particle entities (WPEs) are self-propelled oil droplets on vibrating surfaces.
• WPEs exhibit two-way coupling between particle motion and self-generated waves.
• These systems demonstrate hydrodynamic analogs of quantum phenomena.

Purpose of the Study:

• To theoretically and numerically investigate a dynamical analog of quantum tunneling.
• To explore the behavior of a one-dimensional WPE encountering a Gaussian potential barrier.

Main Methods:

• Utilized an idealized model based on a perturbed Lorenz system.
• Analyzed the dynamics and statistics of barrier crossing.
• Varied initial conditions and system parameters to study transmission probabilities.

Main Results:

• Identified sensitivity and unpredictability in barrier crossing due to WPE velocity fluctuations.
• Observed smooth variations in transmission probability with system parameter changes.
• Detected wave-like features in transmitted and reflected probability density profiles.

Conclusions:

• Nonequilibrium features of the Lorenz system, like transient chaos, drive tunneling dynamics.
• WPEs exhibit complex behaviors analogous to quantum tunneling.
• The study provides insights into the fundamental physics of self-propelled active matter.