Abstract

Zoom link: https://zoom.us/j/98016675669

Active particles consume energy from their environment and turn it into directed motion, leading to remarkable non-equilibrium effects. In this talk I will mostly focus on the run-and-tumble particle (RTP) model, which mimics the persistent motion of bacteria such as E. Coli. I will present recent results for the nonequilibirum steady state that a single RTP reaches when confined by an external harmonic potential. In the first part of the talk, I will present the exact steady state distribution of the position of a particular type of overdamped RTP in two dimensions, whose orientation can take one of four possible values. What enables the exact solution is that, in a proper choice of coordinates, the problem decomposes into two decoupled one-dimensional problems. In the second part of the talk, I will go beyond the overdamped regime, and focus on the limit in which the RTP switches its orientation very fast. I will first recall that typical fluctuations of its position obey a Boltzmann distribution with an effective temperature that can be found exactly. Next, I will consider the large deviations regime which is not described by a Boltzmann distribution, and is instead dominated by a single, most likely trajectory in a coarse-grained dynamical description of the system.

The talk is based on the two recent papers: N. R. Smith, P. Le Doussal, S. N. Majumdar, G. Schehr, arXiv:2207.10445 N. R. Smith, O. Farago, arXiv:2208.06848