Evaluating linear response in active systems with no perturbing field

TL;DR

This paper introduces a novel method to evaluate linear response functions in active particle systems from unperturbed simulations, enabling analysis of their dynamic properties without external perturbations.

Contribution

The authors develop a new approach inspired by Malliavin weights sampling to compute response functions in active systems from unperturbed data, applicable to various interaction potentials.

Findings

Effective temperature decreases with increasing persistence time.

Response functions can be accurately evaluated without external perturbations.

The method is demonstrated on particles in harmonic traps and interacting via screened Coulomb potential.

Abstract

We present a method for the evaluation of time-dependent linear response functions for systems of active Ornstein-Uhlenbeck particles from unperturbed simulations. The method is inspired by the Malliavin weights sampling method proposed by Warren and Allen [Phys. Rev. Lett. 109, 250601 (2012)] for systems of Brownian particles. We illustrate our method by evaluating a linear response function for a single active particle in an external harmonic potential. As an application, we calculate the time-dependent mobility function and an effective temperature, defined through the Einstein relation between the self-diffusion and mobility coefficients, for a system of active particles interacting via a screened-Coulomb potential. We find that this effective temperature decreases with increasing persistence time of the self-propulsion. Initially, for not too large persistence times, it changes rather slowly, but then it decreases markedly when the persistence length of the self-propelled motion becomes comparable with the particle size.