Title: Passive advection in active matter
Abstract: The diffusion process followed by a passive tracer in prototypical active media such as suspensions of active colloids or swimming microorganisms differs significantly from Brownian motion, manifest, e.g., in a greatly enhanced diffusion coefficient and non-Gaussian tails of the displacement statistics. While such characteristic features have been extensively observed in experiments, their theoretical derivation from a first-principles treatment of the tracer-swimmer interactions in various density regimes has been a long-standing open problem. Focusing on dilute active suspensions, I discuss how the effective tracer process can be coarse-grained using a field-theoretic approach leading to a universal Poisson representation of the tracer process valid for general interaction forces and a large class of swimmer dynamics [1]. Mathematically, the tracer is shown to be described by a generalized occupation time problem, for which Feynman-Kac equations can be derived in different perturbative regimes. For the special case of straight-line swimmer motion, the process can be mapped further onto a non-Markovian Poisson process that accounts quantitatively for all of the main empirical observations of the tracer [2]. The theory predicts in particular a long-lived Lévy flight regime of the tracer motion with a non-monotonic crossover between two different power-law exponents. Apart from providing a comprehensive framework for the effective tracer dynamics, the theory provides the first validation of the celebrated Lévy flight model from a physical microscopic dynamics.
[1] A. Baule; PNAS 120,e2308226120 (2023)
[2] K. Kanazawa, T. Sano, A. Cairoli, A. Baule; Nature 579, 364 (2020)
Note: This seminar will be happening in-person only.
Location: Huxley 341, 4-5pm.