When Soft Crystals Defy Newton's Third Law: Nonreciprocal Mechanics and Dislocation Motility.

The effective interactions between the constituents of driven soft matter generically defy Newton's third law. Combining theory and numerical simulations, we establish that six classes of mechanics with no counterparts in equilibrium systems emerge in elastic crystals challenged by nonreciprocal interactions. Going beyond linear deformations, we reveal that interactions violating Newton's third law generically turn otherwise quiescent dislocations into motile singularities which steadily glide though periodic lattices.

Generalized Correlation Profiles in Single-File Systems.

Single-file diffusion refers to the motion in narrow channels of particles which cannot bypass each other, and leads to tracer subdiffusion. Most approaches to this celebrated many-body problem were restricted to the description of the tracer only. Here, we go beyond this standard description by introducing and providing analytical results for generalized correlation profiles (GCPs) in the frame of the tracer. In addition to controlling the statistical properties of the tracer, these quantities fully characterize the correlations between the tracer position and the bath particles density. Considering the hydrodynamic limit of the problem, we determine the scaling form of the GCPs with space and time, and unveil a nonmonotonic dependence with the distance to the tracer despite the absence of any asymmetry. Our analytical approach provides several exact results for the GCPs for paradigmatic models of single-file diffusion, such as Brownian particles with hardcore repulsion, the symmetric exclusion process and the random average process. The range of applicability of our approach is further illustrated by considering (i) extensions to general interactions between particles, (ii) the out-of-equilibrium situation of an initial step of density, and (iii) beyond the hydrodynamic limit, the GCPs at arbitrary time in the dense limit.

Unbinding Transition of Probes in Single-File Systems.

Single-file transport, arising in quasi-one-dimensional geometries where particles cannot pass each other, is characterized by the anomalous dynamics of a probe, notably its response to an external force. In these systems, the motion of several probes submitted to different external forces, although relevant to mixtures of charged and neutral or active and passive objects, remains unexplored. Here, we determine how several probes respond to external forces. We rely on a hydrodynamic description of the symmetric exclusion process to obtain exact analytical results at long times. We show that the probes can either move as a whole, or separate into two groups moving away from each other. In between the two regimes, they separate with a different dynamical exponent, as t^{1/4}. This unbinding transition also occurs in several continuous single-file systems and is expected to be observable.

Universal Long Ranged Correlations in Driven Binary Mixtures.

When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The nature of this "laning transition" is still being debated and, in particular, the pair correlation functions, which are the key observables to quantify this phenomenon, have not been characterized yet. Here, we determine the correlations using an analytical approach based on a linearization of the stochastic equations for the density fields, which is valid for dense systems of soft particles. We find that the correlations decay algebraically along the direction of motion, and have a self-similar exponential profile in the transverse direction. Brownian dynamics simulations confirm our theoretical predictions and show that they also hold beyond the validity range of our analytical approach, pointing to a universal behavior.

Universal Non-Debye Scaling in the Density of States of Amorphous Solids.

At the jamming transition, amorphous packings are known to display anomalous vibrational modes with a density of states (DOS) that remains constant at low frequency. The scaling of the DOS at higher packing fractions remains, however, unclear. One might expect to find a simple Debye scaling, but recent results from effective medium theory and the exact solution of mean-field models both predict an anomalous, non-Debye scaling. Being mean-field in nature, however, these solutions are only strictly valid in the limit of infinite spatial dimension, and it is unclear what value they have for finite-dimensional systems. Here, we study packings of soft spheres in dimensions 3 through 7 and find, away from jamming, a universal non-Debye scaling of the DOS that is consistent with the mean-field predictions. We also consider how the soft mode participation ratio evolves as dimension increases.

Exact spatial correlations in single-file diffusion.

Single-file diffusion refers to the motion of diffusive particles in narrow channels, so that they cannot bypass each other. This constraint leads to the subdiffusion of a tagged particle, called the tracer. This anomalous behavior results from the strong correlations that arise in this geometry between the tracer and the surrounding bath particles. Despite their importance, these bath-tracer correlations have long remained elusive, because their determination is a complex many-body problem. Recently, we have shown that, for several paradigmatic models of single-file diffusion such as the simple exclusion process, these bath-tracer correlations obey a simple exact closed equation. In this paper, we provide the full derivation of this equation, as well as an extension to another model of single-file transport: the double exclusion process. We also make the connection between our results and the ones obtained very recently by several other groups and which rely on the exact solution of different models obtained by the inverse scattering method.

Exact time dependence of the cumulants of a tracer position in a dense lattice gas.

We develop a general method to calculate the exact time dependence of the cumulants of the position of a tracer particle in a dense lattice gas of hardcore particles. More precisely, we calculate the cumulant-generating function associated with the position of a tagged particle at arbitrary time, and at leading order in the density of vacancies on the lattice. In particular, our approach gives access to the short-time dynamics of the cumulants of the tracer position, a regime in which few results are known. The generality of our approach is demonstrated by showing that it goes beyond the case of a symmetric 1D random walk and covers the important situations of (1) a biased tracer, (2) comblike structures, and (3) d-dimensional situations.

Exact closure and solution for spatial correlations in single-file diffusion.

In single-file transport particles diffuse in narrow channels while not overtaking each other. it is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in one dimension. Despite extensive effort, these remained elusive, because they involve an infinite hierarchy of equations. For the symmetric exclusion process, a paradigmatic model of single-file diffusion, we break the hierarchy to unveil and solve a closed exact equation satisfied by these correlations. Beyond quantifying the correlations, the role of this key equation as a tool for interacting particle systems is further demonstrated by its application to out-of-equilibrium situations, other observables, and other representative single-file systems.

Cumulant generating functions of a tracer in quenched dense symmetric exclusion processes.

The symmetric exclusion process (SEP), where particles hop on a one-dimensional lattice with the restriction that there can only be one particle per site, is a paradigmatic model of interacting particle systems. Recently, it has been shown that the nature of the initial conditions-annealed or quenched-has a quantitative impact on the long-time properties of tracer diffusion. However, so far, the cumulant generating function in the quenched case was only determined in the low-density limit and for the specific case of a half-filled system. Here, we derive it in the opposite dense limit with quenched initial conditions. Importantly, our approach also allows us to consider the nonequilibrium situations of (i) a biased tracer in the SEP and (ii) a symmetric tracer in a step of density. In the former situation, we show that the initial conditions have a striking impact, and change the very dependence of the cumulants on the bias.

Pair correlation of dilute active Brownian particles: From low-activity dipolar correction to high-activity algebraic depletion wings.

We study the pair correlation of active Brownian particles at low density using numerical simulations and analytical calculations. We observe a winged pair correlation: While particles accumulate in front of an active particle as expected, the depletion wake consists of two depletion wings. In the limit of soft particles, we obtain a closed equation for the pair correlation, allowing us to characterize the depletion wings. In particular, we unveil two regimes at high activity, where the wings adopt a self-similar profile and decay algebraically. We also perform experiments of self-propelled Janus particles and indeed observe the depletion wings.

N-tag probability law of the symmetric exclusion process.

The symmetric exclusion process (SEP), in which particles hop symmetrically on a discrete line with hard-core constraints, is a paradigmatic model of subdiffusion in confined systems. This anomalous behavior is a direct consequence of strong spatial correlations induced by the requirement that the particles cannot overtake each other. Even if this fact has been recognized qualitatively for a long time, up to now there has been no full quantitative determination of these correlations. Here we study the joint probability distribution of an arbitrary number of tagged particles in the SEP. We determine analytically its large-time limit for an arbitrary density of particles, and its full dynamics in the high-density limit. In this limit, we obtain the time-dependent large deviation function of the problem and unveil a universal scaling form shared by the cumulants.