Field Theory of free Active Ornstein-Uhlenbeck Particles

TL;DR

This paper develops a field theory for free active Ornstein-Uhlenbeck particles, enabling accurate particle tracking and easy extension to include interactions and reactions, advancing theoretical understanding of active matter.

Contribution

It introduces a Doi-Peliti field theory for active Ornstein-Uhlenbeck particles that preserves particle identity and can incorporate potentials and reactions.

Findings

Derived a Doi-Peliti field theory for active particles

Provided a method to diagonalise the Gaussian part of the action

Facilitated calculation of the propagator for these particles

Abstract

We derive a Doi-Peliti field theory for free active Ornstein-Uhlenbeck particles, or, equivalently, free inertial Brownian particles, and present a way to diagonalise the Gaussian part of the action and calculate the propagator. Unlike previous course-grained approaches this formulation correctly tracks particle identity and yet can easily be expanded to include potentials and arbitrary reactions.