English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study two interacting identical run and tumble particles (RTP's) in onedimension. Each particle is driven by a telegraphic noise, and in some cases,also subjected to a thermal white noise with a corresponding diffusion constant$D$. We are interested in the stationary bound state formed by the two RTP's inthe presence of a mutual attractive interaction. The distribution of therelative coordinate $y$ indeed reaches a steady state that we characterize interms of the solution of a second-order differential equation. We obtain theexplicit formula for the stationary probability $P(y)$ of $y$ for two examplesof interaction potential $V(y)$. The first one corresponds to $V(y) \sim |y|$.In this case, for $D=0$ we find that $P(y)$ contains a delta function part at$y=0$, signaling a strong clustering effect, together with a smooth exponentialcomponent. For $D>0$, the delta function part broadens, leading instead to weakclustering. The second example is the harmonic attraction $V(y) \sim y^2$ inwhich case, for $D=0$, $P(y)$ is supported on a finite interval. We unveil aninteresting relation between this two-RTP model with harmonic attraction and athree-state single RTP model in one dimension, as well as with a four-statesingle RTP model in two dimensions. We also provide a general discussion of thestationary bound state, including examples where it is not unique, e.g., whenthe particles cannot cross due to an additional short-range repulsion.

Stationary nonequilibrium bound state of a pair of run and tumble particles