Field-Theory of Active Chiral Hard Disks: A First-Principles Approach to Steric Interactions

TL;DR

This paper develops a first-principles theoretical framework for active chiral hard disks, explicitly incorporating steric interactions and deriving effective hydrodynamic equations that connect to known active matter models.

Contribution

It introduces a systematic derivation of hydrodynamic equations for active chiral disks from microscopic principles, linking to existing models and revealing chirality's impact on activity parameters.

Findings

Derivation of an effective one-body equation for particle positions and angles.

Connection of the hierarchy to known active matter models like Active Model B+.

Chirality can invert the sign of activity parameters.

Abstract

A first-principles approach for active chiral hard disks is presented, that explicitly accounts for steric interactions on the two-body level. We derive an effective one-body equation for the joint probability distribution of ositions and angles of the particles. By projecting onto the angular modes, we write a hierarchy for the lowest hydrodynamic modes, i.e. particle density, polarisation, and nematic tensor. Introducing dimensionless variables in the equations, we highlight the assumptions, which - though inherent - are often included implicit in typical closure schemes of the hierarchy. By considering different regimes of the P{\'e}clet number, the well-known models in active matter can be obtained through our consideration. Explicitly, we derive an effective diffusive description and by going to higher orders in the closure scheme, we show that this first-principles approach results in the recently introduced Active Model B +, a natural extension of the Model B for active processes. Remarkably, here we find that chirality can change the sign of the phenomenological activity parameters.