Boundary layers, transport and universal distribution in boundary driven active systems

TL;DR

This paper provides analytical insights into boundary-driven active systems, revealing unique transport phenomena, spectral properties, and a proposed universality in absorbing boundary problems, highlighting the complex behavior of active particles in nonequilibrium conditions.

Contribution

It introduces new analytical results for run-and-tumble particles with boundary reservoirs, uncovering kinetic boundary layers, spectral structures, and a novel universality in active boundary problems.

Findings

Identification of kinetic boundary layers and nonmonotonous distributions.

Eigenvalue spectrum with two bands and crossover behavior.

Active contribution dominates the bulk, challenging passive models.

Abstract

We discuss analytical results for a run-and-tumble particle (RTP) in one dimension in presence of boundary reservoirs. It exhibits `kinetic boundary layers', nonmonotonous distribution, current without density gradient, diffusion facilitated current reversal and optimisation on tuning dynamical parameters, and a new transport effect in the steady state. The spatial and internal degrees of freedom together possess a symmetry, using which we find the eigenspectrum for large systems. The eigenvalues are arranged in two bands which can mix in certain conditions resulting in a crossover in the relaxation. The late time distribution for large systems is obtained analytically; it retains a strong and often dominant `active' contribution in the bulk rendering an effective passive-like description inadequate. A nontrivial `Milne length' also emerges in the dynamics. Finally, a novel universality is proposed in the absorbing boundary problem for dynamics with short-range colored noise. Active processes driven by active reservoirs may thus provide a common physical ground for diverse and new nonequilibrium phenomena.