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The out-of-equilibrium character of active systems is often twofold, arising from both the activity itself and from non-reciprocal couplings between constituents. A well-established measure to quantify the system's distance from equilibrium…

Statistical Mechanics · Physics 2026-02-13 Kim L. Kreienkamp , Sabine H. L. Klapp

Nonreciprocal active matter systems typically feature an asymmetric role among interacting agents, such as a pursuer-evader relationship. We propose a multi-species nonreciprocal active matter model that is invariant under permutations of…

Statistical Mechanics · Physics 2025-12-23 Chul-Ung Woo , Heiko Rieger , Jae Dong Noh

Magnetic interactions have long served as the most robust and widely used approach for realizing nonreciprocity, with an externally applied magnetic field breaking time-reversal symmetry (TRS) and chiral photon-magnon interactions…

Mesoscale and Nanoscale Physics · Physics 2026-05-12 Jiguang Yao , Ying Yang , Chenyang Lu , Lihua Zhong , Xiaolong Fan , Desheng Xue , C. -M. Hu

A mixture of spinning particles of two different types represents a system where both nonreciprocity and chirality determine the emergent dynamics. In this work we present a minimal model for a two-species mixture of chiral active…

Statistical Mechanics · Physics 2025-10-27 Giulia Pisegna , Suropriya Saha

Out of equilibrium, the lack of reciprocity is the rule rather than the exception. Non-reciprocal interactions occur, for instance, in networks of neurons, directional growth of interfaces, and synthetic active materials. While wave…

Soft Condensed Matter · Physics 2021-04-20 Michel Fruchart , Ryo Hanai , Peter B. Littlewood , Vincenzo Vitelli

Recently, non-reciprocal systems have become a focus of growing interest. Examples occur in soft and active matter, but also in engineered quantum materials and neural (brain) networks. Here, we investigate the impact of non-reciprocity on…

Soft Condensed Matter · Physics 2023-01-10 Kim L. Kreienkamp , Sabine H. L. Klapp

We study a new type of 2D active material that exhibits macroscopic phases with two emergent broken symmetries: self-propelled achiral particles that form dense hexatic clusters, which spontaneously rotate. We experimentally realise active…

Self-propelled particles rarely move in straight lines; environmental interactions, shape asymmetry, and intrinsic torques generically induce curved or fluctuating trajectories. In biological and synthetic systems, this curvature often…

Soft Condensed Matter · Physics 2026-01-06 Diganta Bhaskar , Abhishek Chaudhuri , Anil Kumar Dasanna

We study collective dynamical behavior of active particles with topological interactions and directional reversals. Surprising phenomena are shown to emerge as the interaction relaxation time is varied relative to the reversal rate, such as…

Soft Condensed Matter · Physics 2022-03-11 Kristian Stølevik Olsen , Luiza Angheluta , Eirik Grude Flekkøy

Non-reciprocal systems exhibit diverse dynamical phases whose character depends on the type and degree of non-reciprocity. In this study, we theoretically investigate dynamical structures in a mixture of non-reciprocally aligning polar…

Soft Condensed Matter · Physics 2024-12-20 Kim L. Kreienkamp , Sabine H. L. Klapp

Heterogeneity is ubiquitous in biological and synthetic active matter systems that are inherently out of equilibrium. Typically, such active mixtures involve not only conservative interactions between the constituents, but also…

Soft Condensed Matter · Physics 2024-12-20 Kim L. Kreienkamp , Sabine H. L. Klapp

Active agents are capable of exerting nonreciprocal forces upon one another. For instance, one agent, say $A$, may attract another agent $B$ while $B$ repels $A$. These antagonistic nonreciprocal interactions have been extensively studied…

Quantum Physics · Physics 2025-01-23 Tobias Nadolny , Christoph Bruder , Matteo Brunelli

In this paper, we discuss microscopic models for chiral active particles, i.e., rotating active units that exhibit circular or spinning motion. While non-chiral active particles are typically governed by self-propulsion and conservative…

Soft Condensed Matter · Physics 2025-10-20 Lorenzo Caprini , Alessandro Petrini , Umberto Marini Bettolo Marconi

We study the influence of nonuniform motion of oscillators in a ring chain with nonlocal coupling on their collective dynamics and reveal the mechanism behind the emergence of an atypical chimera state in such systems. The mechanism relies…

Pattern Formation and Solitons · Physics 2025-12-02 Pavel A. Shcherbakov , Lev A. Smirnov , Vasily A. Kostin , Maxim I. Bolotov , Grigory V. Osipov

Polar active particles constitute a wide class of synthetic colloids that are able to propel along a preferential direction, given by their polar axis. Here, we demonstrate a generic self-phoretic mechanism that leads to their spontaneous…

Soft Condensed Matter · Physics 2021-10-27 Marco De Corato , Ignacio Pagonabarraga , Giovanniantonio Natale

Systems of nonlocally coupled oscillators can exhibit complex spatio-temporal patterns, called chimera states, which consist of coexisting domains of spatially coherent (synchronized) and incoherent dynamics. We report on a novel form of…

Adaptation and Self-Organizing Systems · Physics 2018-02-02 Iryna Omelchenko , Oleh E. Omel'chenko , Philipp Hövel , Eckehard Schöll

The interplay between strong long-range interactions and the coherent driving contribute to the formation of complex patterns, symmetry, and novel phases of matter in many-body systems. However, long-range interactions may induce an…

Non-reciprocal interactions in active matter gives rise to a multitude of fascinating phenomena among which are collective oscillatory states without intrinsic particle chirality and active turbulence. Here we show that in a paradigmatic…

Statistical Mechanics · Physics 2026-04-09 Chul-Ung Woo , Jae Dong Noh , Heiko Rieger

Complex systems out of equilibrium often experience intermittent oscillations between quiescent and highly dynamic states. The type of intermittency depends on how energy is pumped into the system, and how it is dissipated. While…

Soft Condensed Matter · Physics 2026-02-23 Zhicheng Shu , Wei-Chih Li , Wentao Yu , Justin C. Burton

Non-reciprocal interactions between scalar fields that represent the concentrations of two active species are known to break the parity and time-reversal (PT) symmetries of the equilibrium state, as manifested in the emergence of travelling…

Statistical Mechanics · Physics 2022-09-01 Suropriya Saha , Ramin Golestanian
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