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Interacting Persistent Random Walkers

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SPL - New statistical physics in living matter: non equilibrium states under adaptive control

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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