The Anomalous Transport of Tracers in Active Baths

TL;DR

This paper investigates the long-time behavior of tracers in one-dimensional active baths, revealing shape-dependent anomalous diffusion, superdiffusive behavior, and the active enhancement of motion, challenging traditional models of passive tracer dynamics.

Contribution

It introduces a detailed analysis of how tracer symmetry and shape influence long-time dynamics and friction in active baths, highlighting novel effects like superdiffusion and negative friction.

Findings

Damping and noise correlations have long-time tails depending on tracer symmetry.

Shape asymmetry induces ratchet effects and superdiffusion.

Active particles can enhance tracer motion, leading to negative friction.

Abstract

We derive the long-time dynamics of a tracer immersed in a one-dimensional active bath. In contrast to previous studies, we find that the damping and noise correlations possess long-time tails with exponents that depend on the tracer symmetry. For generic tracers, shape asymmetry induces ratchet effects that alter fluctuations and lead to superdiffusion and friction that grows with time when the tracer is dragged at a constant speed. In the singular limit of a completely symmetric tracer, we recover normal diffusion and finite friction. Furthermore, for small symmetric tracers, the active contribution to the friction becomes negative: active particles enhance motion rather than oppose it. These results show that, in low-dimensional systems, the motion of a passive tracer in an active bath cannot be modeled as a persistent random walker with a finite correlation time.