Gaussian fluctuations of non-reciprocal systems

TL;DR

This paper investigates linear non-reciprocal systems with noise, revealing how non-reciprocity influences stability, fluctuations, and noise characteristics, with implications for understanding non-equilibrium states of matter.

Contribution

It provides a detailed analysis of stability, exceptional points, and noise behavior in simple linear non-reciprocal models, advancing the theoretical understanding of such systems.

Findings

Non-reciprocity can enhance system stability.

Exceptional points lead to increased fluctuations.

Strong non-reciprocity causes finite-momentum instability.

Abstract

Non-reciprocal systems can be thought of as disobeying Newtons third law - an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest towards such systems. On a fundamental level, they can be a basis of describing non-equilibrium and active states of matter, with applications ranging from physics to social sciences. However, often the first step to understanding complex nonlinear models is to linearize about the steady states. It is thus useful to develop a careful understanding of linear non-reciprocal systems, similar to our understanding of Gaussian systems in equilibrium statistical mechanics. In this work we explore simplest linear non-reciprocal models with noise and spatial extent. We describe their regions of stability and show how non-reciprocity can enhance the stability of a system. We demonstrate the appearance of exceptional and critical exceptional points with the respective enhancement of fluctuations for the latter. We show how strong non-reciprocity can lead to a finite-momentum instability. Finally, we comment how non-reciprocity can be a source of colored, $1/f$ type noise.