Diffraction and interference with run-and-tumble particles

TL;DR

This paper explores quantum-active run-and-tumble particles, modeling their diffraction and interference behaviors, revealing how they produce wave-like patterns and time-of-arrival statistics, with implications for understanding electron dynamics.

Contribution

It introduces a wave function-driven model for run-and-tumble particles, connecting classical bacterial motion to quantum electron behavior and demonstrating interference phenomena.

Findings

Visualization of electron trajectories in diffraction experiments

Derivation of time-of-arrival statistics for electrons

Observation of interference patterns in non-quantum guidance regimes

Abstract

Run-and-tumble particles, frequently considered today for modeling bacterial locomotion, naturally appear outside a biological context as well, e.g. for producing waves in the telegraph process. Here, we use a wave function to drive their propulsion and tumbling. Such quantum-active motion realizes a jittery motion of Dirac electrons (as in the famous Zitterbewegung): the Dirac electron is a run-and-tumble particle, where the tumbling is between chiralities. We visualize the trajectories in diffraction and double slit experiments for electrons. In particular, that yields the time-of-arrival statistics of the electrons at the screen. Finally, we observe that away from pure quantum guidance, run-and-tumble particles with suitable spacetime-dependent parameters produce an interference pattern as well.