Abstract

In this talk I will consider persistent random walkers, also known as run and tumble particles, which are emerging as a fundamental microscopic model of active matter. I will first review the properties of a single persistent walker and show how it interpolates between ballistic and diffusive motion. The dynamical spectrum of a persistent random walker exhibits `exceptional points’ indicating dynamical transitions – a familiar example of an exceptional point is the critical damping of the simple harmonic oscillator. I will then consider the case of two persistent random walkers that interact through an exclusion interaction. An exact expression for the stationary state of two such walkers on a periodic lattice reveals how the particles jam and generate an effective attractive potential. The full spectrum of the two-particle problem can also be computed and again exhibits exceptional points, which correspond to dynamical transitions in the relaxation time. Finally, I will discuss a more general `recoil’ interaction between the persistent walkers and show how tuning the persistence length can generate attractive or repulsive effective interactions.