Bulletin of the American Physical Society
2024 APS March Meeting
Monday–Friday, March 4–8, 2024; Minneapolis & Virtual
Session M29: NonReciprocity in Soft and Active Matter IFocus

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Sponsoring Units: DSOFT DBIO GSNP Chair: Daniel Sussman, Emory University Room: 101J 
Wednesday, March 6, 2024 8:00AM  8:12AM 
M29.00001: Generalized timereversal symmetry and effective theories for nonequilibrium matter Jack H Farrell, Xiaoyang Huang, Aaron J Friedman, Isabella M Zane, Paolo Glorioso, Andrew Lucas The past decade has witnessed the development of systematic effective theories for dissipative thermal systems. In this talk, I will describe an analogous effective theory framework that applies to the classical stochastic dynamics of nonequilibrium systems. This approach applies to a range of examples, including nonreciprocal (predatorprey) dynamics, dissipative and driven rigidbody motion, and active chiral fluids and solids. Many of these systems exhibit a generalized timereversal symmetry, which plays a crucial role within our formalism, and which in many cases can be implemented within the MartinSiggiaRose path integral. This effective theory formalism yields generalizations of the fluctuationdissipation theorem and the second law of thermodynamics valid out of equilibrium. By stipulating a stationary distribution and a set of symmetries—rather than postulating the stochastic equations of motion directly—the effective theory framework provides an alternative route to building phenomenological models of driven and active matter. 
Wednesday, March 6, 2024 8:12AM  8:24AM 
M29.00002: Effective field theory approach to odd elasticity Isabella M Zane, Jack H Farrell, Xiaoyang Huang, Aaron J Friedman, Andrew Lucas We have developed an effective field theory (EFT) framework applicable to active, nonequilibrium systems. Our approach to applying the EFT paradigm in the context of active matter departs from traditional methods that start with equations of motion. Instead, we postulate the form of the nonequilibrium steady state, which captures equaltime correlations. This approach offers an alternative pathway for constructing phenomenological models for driven and active matter. In this work, we apply our EFT formalism to problems in active solids—solids with active, nonconservative microscopic interactions that enable the material to perform work on its environment through quasistatic cycles of deformations. In the realm of odd elasticity, these active components contribute to the odd component of the static elastic modulus tensor. Specifically, we apply our formalism to a paper by Scheibner et al. [1], which established the equations of motion for odd elastic solids by postulating the most general stress tensor consistent with symmetry principles. By assuming there must be some notion of stationarity in this system, we discover additional constraints on certain active moduli. Our approach brings to light subtleties related to the nature of noise and time reversal symmetry breaking, leading to nontrivial results that have previously been overlooked. 
Wednesday, March 6, 2024 8:24AM  8:36AM 
M29.00003: Optimal design of odd elastic metamaterials Jack Binysh, Guido C Baardink, Jonas Veenstra, Anton Souslov, Corentin Coulais Nonreciprocal interactions in active solids yield elastic moduli forbidden in equilibrium. These odd moduli offer a bottomup approach to designing autonomous materials that spontaneously crawl, roll or swim. However, current schemes for designing odd materials are typically overactuated, using excessively many active elements. This overactuation limits the feasibility of largescale experimental realisations, and invites the challenge of rational design: how can microscopic nonreciprocity be optimally converted into macroscale odd response? 
Wednesday, March 6, 2024 8:36AM  9:12AM 
M29.00004: Nonreciprocity permits novel dynamics in living and active topological systems Invited Speaker: Evelyn Tang Living and active systems exhibit various emergent dynamics during system regulation, growth, and motility. However, how robust dynamics arises from stochastic components remains unclear. Towards understanding this, I develop topological theories that support robust edge currents, effectively reducing the system dynamics to a lowerdimensional subspace. I will introduce stochastic networks in molecular configuration space that model different systems from a circadian clock to ring attractors. The edge localization results in new properties, e.g., the clock demonstrates increased precision with simultaneously decreased cost. Crucially, we find that unlike in quantum systems, nonreciprocity is strictly necessary for edge states and strong localization in stochastic topological systems. Our work indicates new pathways for the design and control of active systems and their dynamics. 
Wednesday, March 6, 2024 9:12AM  9:24AM 
M29.00005: Tuning nonreciprocal pattern Xiaofei Guo, Jonas Veenstra, Corentin Coulais Reciprocity is a fundamental principle guiding the behavior of the majority of physical systems. However, when these systems are out of equilibrium, a lack of reciprocity becomes more common. In recent years, researchers have extensively explored nonreciprocity across various systems. Nevertheless, the vast majority of tend to converge towards a single specific state. Here, we demonstrate the potential of multiple states in nonreciprocity active metamaterials, both theoretically and experimentally. By manipulating the initial states, we have the capability to specifically target a desired final state. Furthermore, when the system is initiated from random noise, countless mixed states, combinations of the basic states over time or space, can also emerge. We foresee that exploring multiple nonreciprocal states will pave the way for a deeper understanding of active matter and living matter, and open avenues in the fields of wave propagations, versatile soft robots and metamaterials. 
Wednesday, March 6, 2024 9:24AM  9:36AM 
M29.00006: Lorentz Reciprocal Theorem in Fluids with Odd Viscosity Yuto Hosaka, Ramin Golestanian, Andrej Vilfan The Lorentz reciprocal theoremthat is used to study various transport phenomena in hydrodynamicsis violated in chiral active fluids that feature odd viscosity with broken timereversal and parity symmetries. Here we show that the theorem can be generalized to fluids with odd viscosity by choosing an auxiliary problem with the opposite sign of the odd viscosity [1]. To demonstrate its applicability, we use the thorem to determine the swimming velocity of two categories of microswimmers in a Stokes fluid with odd viscosity: first to swimmers with an imposed slip velocity on their surface and then to swimmers with a prescribed tangential force density. We solve both problems for spherical swimmers in a 3D fluid as well as diskshaped swimmers in 2D. In both cases, we show that odd viscosity does not affect the motion of swimmers with prescribed surface velocity, but it does affect those with prescribed propulsive forces. A particularly interesting case is a "twister" which propels itself by exerting only a torque dipole on the fluid. 
Wednesday, March 6, 2024 9:36AM  9:48AM 
M29.00007: Nonreciprocal stochastic topological networks show new properties as compared to quantum counterparts Ziyin Xiong, Aleksandra Nelson, Evelyn Tang Stochastic topological systems draw from topological invariants first developed for quantum systems. While stochastic and quantum systems can share the same invariant in the bulk, their spectra differ under open boundary conditions, leading to new properties. We systematically investigate how spectra in both systems differ. Solving the spectrum analytically using Chebyshev polynomials, we find that in a 1D uniform chain and SSH model with even sites, the stochastic spectrum is given by a onesite smaller quantum system. The spectral differences are most prominent in small system sizes and large nonreciprocity, where quantum states converge while the gap increases between the steadystate and the slowest decaying state in stochastic systems. In the 2D SSH model, we find that exceptional points emerge in different areas of the spectrum in the topological phase. More broadly, this work characterizes unique physical properties that emerge from identical networks described by Laplacian and adjacency matrices respectively. 
Wednesday, March 6, 2024 9:48AM  10:00AM 
M29.00008: Active Boltzmann equation for selfpropelled particles with nonreciprocal interactions HorstHolger Boltz, Jakob Mihatsch, Rüdiger Kürsten, Thomas Ihle We study models of selfpropelled particles with alignment interactions by means of an active Boltzmann equation. To this end, we evaluate the collision integral directly based on the microscopic equations of motion. This kinetic theory is founded on the assumption of onesided molecular chaos, a refinement to the molecular chaos assumption underlying commonly employed meanfield approaches. We have introduced the methods for Vicsektype active particles with antialignment that allows for an asymptotically exact analytical solution. One direct application is the extraction of the selfdiffusion coefficient which cannot be done to meanfield order. This exact solution has then been used to study the behaviour of binary mixtures with nonreciprocal and chiral interactions. In addition to analytical approaches, the methodology allows for numerical calculation of the collision integral in systems that cannot be treated analytically which we use to evaluate the beyond meanfield corrections to the flocking transition under noise. 
Wednesday, March 6, 2024 10:00AM  10:12AM 
M29.00009: Multicomponent active diffusion YuJen Chiu, Ahmad K Omar, Daniel Evans Nonreciprocal interactions are ubiquitous in the natural and living world and can endow systems with properties that have no analog in passive materials. A familiar example of a nonreciprocal interaction is the socalled "predatorprey" interaction whereby one entity (the predator) feels an attractive force towards the other while the other (the prey) is repelled. These effective nonreciprocal interactions can emerge from a host of complex factors and can have farreaching implications on collective phenomena, phase transitions, and pattern formation. In this talk, we present a dynamical framework for determining the stability of multicomponent active systems. We present phenomenological linear transport relations and derive GreenKubo relations for the linear transport coefficients that govern the stability of these nonequilibrium systems. For a large class of systems, we can further relate these transport coefficients to mechanical variables, providing a simple criterion for the emergence of traveling phases. Our perspective thus provides a multiscale framework for understanding nonreciprocal phase transitions with multiple conserved order parameters. We demonstrate the utility of this perspective by applying it to two model active systems and predicting the emergence of both stationary and traveling phase transitions. 
Wednesday, March 6, 2024 10:12AM  10:24AM 
M29.00010: Odd diffusivity and odd mobility in a system with equilibrium structure Grzegorz Szamel, Federico Ghimenti, Ludovic Berthier, Frederic van Wijland Odd transport coefficients may generally appear in systems with broken timereversal and parity symmetry [1,2]. Typical examples are systems that are driven at the level of individual constituents, and thus have stationary state distributions that are not known explicitly. This makes the analysis of these systems challenging. Here we consider a system of interacting Brownian particles evolving under the influence of forces that have components transverse to energy gradients [3]. The evolution breaks the timereversal and parity symmetry but its stationary distribution coincides with the equilibrium distribution. We analyze the tracer dynamics and derive expressions for the selfdiffusion and mobility coefficients, including their odd components. A modecoupling approximation predicts that the ratio of the odd diffusion and odd mobility diverges at the dynamic glass transition, which implies an extreme violation of the Einstein relation. 
Wednesday, March 6, 2024 10:24AM  10:36AM 
M29.00011: Spacetime symmetry and nonreciprocal transport in dynamic mechanical systems Abhijeet Melkani, Jayson J Paulose Active mechanical structures whose parameters are modulated in space and time harbor wave phenomena, such as amplification and nonreciprocal transport, that are forbidden in passive materials. One such phenomenon is parametric resonance, which generates exponentially growing or decaying oscillations when parameters are modulated periodically in time. While parametric resonance of individual oscillators is well understood, identifying the conditions for parametric resonance in systems of coupled oscillators remains challenging. In this talk, we will identify and use the nonHermitian internal symmetries arising from the realvalued and symplectic nature of classical mechanics to determine these parametric resonance conditions. Upon including external symmetries, we find the conditions for modes to be protected from resonating at certain modulation frequencies where they were expected to resonate in the absence of the external symmetry. In particular, we analyze systems with spacetime symmetry where the system remains invariant after a combination of discrete translation in both space and time. For such systems, we identify a combined spacetime translation operator that provides more information about the system than the Floquet operator does, and use it to derive conditions for nonreciprocal wave amplification in mechanical metamaterials. Our results establish an exact theoretical framework based on symmetries to engineer nonreciprocal transport in outofequilibrium systems. 
Wednesday, March 6, 2024 10:36AM  10:48AM 
M29.00012: Molecular modelling of odd viscoelastic fluids Pawel Matus, Piotr Surowka, Ruben Lier In materials that break chiral symmetry, the stress response to applied strain can contain unusual coefficients dubbed odd viscosity (in fluids) or odd elasticity (in solids), both of which can be seen as special cases of a general phenomenon of odd viscoelasticity. In this talk, I will describe and analyze the first known microscopic model that produces an odd viscoelastic fluid. The model consists of a collection of dumbbells suspended in a fluid, with the beads of the dumbbells featuring an active driving system that exerts torque on the dumbbells. After coarsegraining the model we analytically calculate the odd viscoelastic coefficients and corroborate the findings using molecular dynamics simulations. 
Wednesday, March 6, 2024 10:48AM  11:00AM 
M29.00013: Nonreciprocal alignment can induce asymmetric clustering in active repulsive mixtures Kim L Kreienkamp, Sabine H. L. Klapp It is now well established that nonreciprocal systems exhibit intriguing, novel dynamical phases, the characteristics of which are shaped by the type and degree of nonreciprocity [13]. Here, we study a paradigmatic model of nonreciprocal active matter, namely a binary mixture of motile particles with completely symmetric repulsive interactions and nonreciprocal alignment couplings [3]. Using a combination of hydrodynamic theory, linear stability analysis, and particlebased simulations, we find dynamical, asymmetrical clustering situations, in which weakly polarized clusters form out of only one of the two species. Importantly, these asymmetric clusters emerge even though the isotropic repulsive interactions do not distinguish one species. Instead, the clustering is driven solely by nonreciprocal orientational couplings. For systems with antagonistic (anti)alignment couplings, the resulting singlespecies clusters move and chase more dilute accumulations of the other species. We present a full nonequilibrium phase diagram in the parameter space of interspecies coupling strengths and compare with particlebased simulations, highlighting the impact of nonreciprocity on various scales. 
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