Active actions: effective field theory for active nematics

TL;DR

This paper develops a comprehensive effective field theory framework for active nematics, elucidating how activity influences fluctuations and dynamics, and providing a foundation for understanding a broad class of active matter systems.

Contribution

It introduces a general, unambiguous effective field theory for active nematics, extending fluctuation-dissipation relations to active systems in two dimensions.

Findings

Predicts the relationship between fluctuations and equations of motion in active nematics.

Generalizes fluctuation-dissipation relations for active matter.

Provides a theoretical foundation applicable to various active systems.

Abstract

Active matter consumes energy from the environment and transforms it into mechanical work. Notable examples from biology include cell division, bacterial swarms, and muscle contraction. In this work, we investigate the nature of active matter systems using the powerful effective field theory toolbox. This allows us to construct the most general theory without ambiguity up to a given order in the derivative expansion. Our primary focus is active nematics -- liquid crystal systems that spontaneously break rotational but not translational symmetry -- in two spatial dimensions. (Such spontaneous symmetry breaking is allowed if the nematic is embedded in a higher dimensional space.) While we focus on this one particular class of physical system, the tools developed here can in principle be applied to any active matter system. Our theories give unambiguous predictions for the relationship between fluctuations and equations of motion in the presence of activity, generalizing the standard fluctuation-dissipation relations characteristic of passive systems.