Critical active dynamics is captured by a colored-noise driven field theory

TL;DR

This paper investigates the violation and restoration of the Fluctuation-Dissipation Theorem in active particles near a critical point, introducing a novel field theory with correlated noise that captures critical behavior.

Contribution

It develops a new field-theoretical model with space-time correlated noise to describe critical active matter, showing it preserves equilibrium critical exponents.

Findings

Strong FDT violation at short scales

FDT is restored at large scales

Correlated noise captures critical active matter features

Abstract

We numerically investigate the correlation function, the response and the breakdown of the Fluctuation-Dissipation Theorem (FDT) in active particles close to the motility-induced critical point. We find a strong FDT violation in the short time and wavelength regime, where the response function has a larger amplitude than the fluctuation spectrum. Conversely, at larger spatiotemporal scales, the FDT is restored and the critical slowing-down is compatible with the Ising universality class. Building on these results, we develop a novel field-theoretical description employing a space-time correlated noise which qualitatively captures the numerical results already at the Gaussian level. By performing a one-loop renormalization group analysis we show that the correlated noise does not change the critical exponents with respect to the equilibrium. Our results demonstrate that a correlated noise field is a fundamental ingredient to capture the features of critical active matter at the coarse-grained level.