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 intermittency is usually driven by stochastic noise or external forcing, energy can also be sourced from field-mediated interactions between particles, which are often nonreciprocal and effectively violate Newton's 3rd law. Here we demonstrate how nonreciprocal interactions produce intermittency in clusters of charged micron-sized particles confined in a plasma sheath. Through three-dimensional particle tracking, we observe that vertical oscillations, induced by fluctuations of the plasma environment, can be parametrically coupled to the horizontal modes. Experiments and simulations show that nonreciprocal interactions strongly amplify this parametric coupling, creating a positive feedback loop that drives explosive growth of both the horizontal and vertical modes. This mechanism triggers abrupt melting transitions from an ordered cluster to an ergodic gas-like state, and leads to intermittent switching between states over long time scales. Overall, our work identifies nonreciprocal interactions as a key mechanism through which strongly coupled finite systems transform interaction-mediated activity into dynamical nonequilibrium states.
Understanding how systems organize and function far from equilibrium remains one of the central challenges in statistical and soft matter physics. Nonequilibrium systems typically break detailed balance, continuously extract energy from their surroundings, and sustain entropy production [1,2]. As a result, they can exhibit dynamics and functionalities that are inaccessible in equilibrium. Nonequilibrium systems are ubiquitous in nature, spanning length scales from molecular motors to animal flocks [3][4][5][6][7][8]. Similar principles are increasingly exploited in the laboratory to design synthetic materials, including colloidal assemblies that self-organize into dynamical structures [9][10][11][12][13][14][15][16] and active materials composed of workgenerating units that support self-excited oscillations and locomotion [17][18][19][20][21][22].
A many-body system of interacting particles can be driven far from equilibrium by making each particle active. Here, “activity” typically means that individual constituents internally consume energy to generate motion [1,23,24]. In nature, microswimmers such as E. coli convert chemical energy from ATP hydrolysis into self-propulsion [24,25]. Nonliving particles can acquire autonomous motion when energy is supplied externally through phoretic mechanisms such as light activation [9,10], chemical reactivity [26,27], or DC electric fields [11][12][13]. Collections of such self-propelled units are referred to as active matter, which exhibits emergent behavior arising from their persistent energy consumption at the single-particle level, while the interactions between particles can be pairwise and reciprocal [23]. * justin.c.burton@emory.edu Even without single-particle activity, interacting particles can exhibit rich collective behavior when the interactions themselves become nonreciprocal, i.e., F ij ̸ = -F ji , effectively violating Newton’s 3rd law [28,29]. Such nonreciprocity naturally arises when forces are mediated through a driven environment. For example, wavemediated interactions can support emergent collective activity, allowing two or more otherwise passive particles to harness energy from scattered waves and move coherently [30,31]. This “social activity” depends strongly on the spatial configuration of particles, and will generally involve non-pairwise interactions [32][33][34]. In fact, many living systems that exhibit flocking, schooling, and other coordinated motion involve both single particle activity and nonreciprocal, field-mediated interactions [23,[35][36][37].
Significant progress has been made in understanding collective behavior from nonreciprocity in the thermodynamic limit, such as the emergence of spatiotemporal oscillations and dynamical patterns that are inaccessible in equilibrium systems [38][39][40][41][42][43][44][45][46]. However, much less is known about how nonreciprocity affects the dynamics of finite systems with only a few coupled degrees of freedom where coarse-grained descriptions become insufficient. For such systems, analytical and numerical results have shown that nonreciprocity alone can break detailed balance and induce energy and information flow [29,47,48]. However, experimental data remains limited, particularly when steady states do not exist, and dynamics are complex.
In this work, we experimentally demonstrate that nonreciprocal interactions between just two particles can generate unique nonequilibrium states marked by intermittent bursts of activity that drive transitions between quiescent and dynamical phases. Our experiments use a tractable model system: charged microparticles con- The charged dust particles are levitated above the electrode and confined within the center of the electrode due to the electric field gradient. The ions stream towards the electrode and form the ion wakes below the particles which make the interactions between particles effectively nonreciprocal. The down-streaming ions also drift in the azimuthal direction due to the magnetic field, which induces the cluster rotation. Note that the ion drift velocity is much smaller than the streaming velocity.
fined in a plasma sheath, commonly referred to as a dusty plasma. The levitated particles self-assemble into quasi two-dimensional (2D) crystalline clusters [49][50][51], yet these clusters remain intrinsically far from equilibrium. Fluctuations in the surrounding plasma, such as variations in electric field and particle charge, introduce stochastic forcing that excites particle oscillations [52][53][54][55][56][57]. In addition, their plasma-mediated interactions are intrinsically nonreciprocal. When ions stream past a negatively charged particle, they form an asymmetric region of enhanced ion density below the particle (ion wake), leading to effective forces that violate action-reaction symmetry [58][59][60][61]. There are several consequences of this nonreciprocity in dusty plasmas, including coupling between oscillation modes [62][63][6
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