Séminaire du LPTMS : Martin Evans (Edinburgh University)

Interacting Persistent Random Walkers

Martin Evans (University of Edinburgh)

Hybrid: onsite seminar + zoom.
Register in advance for this meeting:
https://cnrs.zoom.us/meeting/register/tJcldumrpjkqGdWYFLoHp0xVov_xj7sDwbHh
After registering, you will receive a confirmation email containing information about joining the meeting.

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.

Date/Time : 22/11/2022 - 11:00 - 12:00

Location : Salle des séminaires du FAST et du LPTMS, bâtiment Pascal n°530