Coupling an elastic string to an active bath: the emergence of inverse damping

TL;DR

This paper models an elastic string coupled to active particles, revealing conditions under which negative friction causes wave instabilities, with explicit formulas and simulation validation.

Contribution

It derives exact expressions for the induced Langevin-Klein-Gordon dynamics with a weak coupling expansion, highlighting the frenetic contribution to negative damping.

Findings

Frenetic contribution can induce negative friction leading to wave instability.

Explicit formulas for streaming, friction, and noise variance are derived.

Simulations confirm initial growth driven by anti-damping.

Abstract

We consider a slow elastic string with Klein-Gordon dynamics coupled to a bath of run-and-tumble particles. We derive and solve the induced Langevin-Klein-Gordon string dynamics with explicit expressions for the streaming term, friction coefficient, and noise variance. These parameters are computed exactly in a weak coupling expansion. The induced friction is a sum of two terms: one entropic, proportional to the noise variance as in the Einstein relation for a thermal equilibrium bath, and a frenetic contribution that can take both signs. The frenetic part wins for higher bath persistence, making the total friction negative, and hence creating a wave instability akin to inverse Landau damping. However, this acceleration decreases and eventually disappears when the propulsion speed of the active particles becomes much higher. Detailed simulations confirm the initial growth driven by this anti-damping.