# Active Particle Condensation by Nonreciprocal and Time-delayed Interactions

## TL;DR

This paper investigates how non-reciprocal and delayed interactions among self-propelling agents lead to spontaneous condensation into pinned drops, revealing a novel stable flocking state without attractive forces.

## Contribution

It demonstrates that non-reciprocal vision-based interactions combined with delays induce a new condensed flocking phase in active matter systems.

## Key findings

- Agents form stable, pinned drops without attraction or confinement.
- The condensed state is stabilized by system noise.
- The phenomenon arises from non-reciprocal and delayed interactions.

## Abstract

We consider flocking of self-propelling agents in two dimensions, each of which communicates with its neighbors within a limited vision cone. Also, the communication occurs with some delay. The communication among the agents are modeled by Vicsek rules. In this study we explore the effect of non-reciprocal interaction among the agents, induced by their vision cone, together with the delayed interactions on the dynamical pattern formation within the flock. We find that under these two influences and without any position based attractive interactions or confining boundaries, the agents can spontaneously condense into drops. Though the agents are in motion within the drop, the drop as whole is virtually pinned in space. We also find that this novel state of the flock has a well defined order stabilized by the noise present in the system.