Nonreciprocal many-body physics

TL;DR

This review explores the concept of nonreciprocity across various physical systems, highlighting universal phenomena like phase transitions and noise amplification in many-body contexts, and discusses open questions in the field.

Contribution

It provides a comprehensive overview of nonreciprocity, unifying diverse manifestations and analyzing their collective phenomena in many-body systems.

Findings

Identification of universal consequences of nonreciprocity

Analysis of nonreciprocal phase transitions

Discussion of non-normal amplification effects

Abstract

Reciprocity is a fundamental symmetry present in many natural phenomena and engineered systems. Distinct situations where this symmetry is broken are typically grouped under the umbrella term "nonreciprocity", colloquially defined by: the action of A on B $\neq$ the action of B on A. In this review, we elucidate what nonreciprocity is by providing an introduction to its most salient classes: nonvariational dynamics, violations of Newton's third law, broken detailed balance, nonreciprocal responses and nonreciprocity of arbitrary linear operators. Next, we point out where to find these manifestations of non-reciprocity, from ensembles of particles with field mediated interactions to synthetic neural networks and open quantum systems. Given this breadth of contexts and the lack of an all-encompassing definition, it makes it all the more intriguing that some general conclusions can be gathered, when distinct definitions of nonreciprocity overlap. We explore what these universal consequences are with a special emphasis on collective phenomena that arise in nonreciprocal many-body systems. The topics covered include nonreciprocal phase transitions and non-normal amplification of noise and perturbations. We conclude with some open questions.