Diffraction and interference with run-and-tumble particles

Abstract

Run-and-tumble particles, frequently considered today for modeling bacterial locomotion, naturally appear outside a biological context as well. Here, we consider them in a quantum mechanical relation, using 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 electron trajectories in single and double slit experiments and discuss their dependence on the spin-direction. 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.