arXiv subjects

Raphaël Voituriez

Publications and source records attributed to Raphaël Voituriez.

At least 19 recordsLinked to original sources

arXiv2026

Collective dynamics of trail-interacting particles

Trail interactions occur when past particle trajectories bias future motion, rendering the system out of thermodynamic equilibrium. While such systems are abundant in nature, their understanding is limited to the single-particle level or phenomenological mean-field theories. Here, we introduce a minimal model of many trail-interacting particles, which extends this paradigm to the fluctuating collective level in arbitrary dimension. Particles diffuse while depositing long-lasting repelling/attracting trails that act as a shared memory field, coupling their dynamics across time and space. Using stochastic density functional theory, we derive fluctuating hydrodynamic equations and analyze analytically and numerically the resulting behaviors. We show that memory, coupled with fluctuations, fundamentally reshapes collective dynamics; In the repulsive case, the particle density displays superdiffusive spreading for $d=1$ and diffusive spreading for $d\geq2$, characterized by transient clustering and ballistic motion; In the attractive case, the system condensates in finite time into frozen, localized states. Our results establish general principles for trail-interacting systems and reveal how persistent fields generate novel instabilities and drive self-organization.

cond-mat.stat-mech↗

arXiv2026

Disordered Yet Directed: The Emergence of Polar Flocks with Disordered Interactions

Flocking is a prime example of how robust collective behavior can emerge from simple interaction rules. The flocking transition has been studied extensively since the inception of the original Vicsek model. Here, we introduce a self-propelled particle model with quenched disorder in the pairwise alignment interaction couplings akin to a spin-glass model. We find that increasing the variance of the coupling distribution can promote (rather than destroy) the emergence of global polar order. In particular, we show that our model can display a flocking phase even when the majority of the interaction couplings are antialigning. Activity is the key ingredient to reduce frustration in the system as it allows local particle clustering combined with self-organization of the particles to favor neighborhoods with strong cooperative interactions.

cond-mat.soft↗

arXiv2026

Large volume statistics of first-passage observables of $d$-dimensional Jump Processes

First-passage observables (FPO) are central to understanding stochastic processes in confined domains, with applications spanning chemical reaction kinetics, foraging behavior, and molecular transport. While extensive analytical results exist for continuous processes, discrete jump processes - crucial for describing empirically observed dynamics - remain largely unexplored in this context. This paper presents a comprehensive framework to systematically evaluate FPO for $d$-dimensional isotropic jump processes, in the asymptotic regime of large confining domains, capturing both geometric and dynamical observables. Leveraging the connection between jump processes and their continuous counterparts, we address the limitations of continuous approximations in capturing discrete effects, particularly near absorbing boundaries. Our method unifies FPO calculations across edge and bulk regimes, providing explicit asymptotic expressions for key observables, such as splitting probabilities, distributions of escape points, and first-passage time distributions in complex geometries. We illustrate our approach with paradigmatic examples, including splitting probabilities in two-dimensional eccentric disks and mean exit times for heavy-tailed processes. These results underscore the broad applicability of our framework to diverse physical systems, offering novel insights into the complexity of discrete dynamics in bounded geometries.

cond-mat.stat-mech↗

arXiv2026

Exact collective first-passage statistics of N trail-interacting walkers

Memory encoded in the environment mediates interactions between active agents, from trail-following organisms to synthetic active matter depositing persistent tracks. Although such memory is known to strongly affect transport, its consequences for collective first-passage phenomena remain largely unexplored. Here we study $N$ one-dimensional random walkers interacting through a shared trail field. We characterize the $k^{\rm th}$ (among $N$) arrival time at a fixed target, and the probability that exactly $k$ walkers in $[0,1]$ reach one boundary before the other. For the broad class of self-interacting walkers with a saturating response to the trail, we derive exact expressions for the corresponding persistence exponents and splitting probabilities. Strikingly, despite the strong history-dependent correlations generated by the common environment, splitting probabilities are exactly identical whether walkers explore simultaneously or one after another. This invariance breaks down for nonsaturating trail interactions. Our results follow from an exact representation of the collective trail field and establish a framework for first-passage phenomena in systems coupled through persistent environmental memory.

cond-mat.stat-mech↗

arXiv2025

Emergent memory in cell-like active systems

Active systems across scales, ranging from molecular machines to human crowds, are usually modeled as assemblies of self-propelled particles driven by internally generated forces. However, these models often assume memoryless dynamics and no coupling of internal active forces to the environment. Here, guided by the example of living cells, which have recently been shown to display multi-timescale memory effects, we introduce a general theoretical framework that goes beyond this paradigm by incorporating internal state dynamics and environmental sensing into active particle models. We show that when the self-propulsion of an agent depends on internal variables with their own complex dynamics - modulated by local environmental cues - environmental memory spontaneously emerges and gives rise to new classes of behaviours. These include memory-induced responses, adaptable localization in complex landscapes, suppression of motility-induced phase separation, and enhanced jamming transitions. Our results demonstrate how minimal information processing capabilities, intrinsic to non-equilibrium agents with internal states like living cells, can profoundly influence both individual and collective behaviours. This framework bridges cell-scale activity and large-scale intelligent motion in cell assemblies, and opens the way to the quantitative analysis and design of systems ranging from synthetic colloids to biological collectives and robotic swarms.

cond-mat.stat-mech↗

arXiv2025

Flips Reveal the Universal Impact of Memory on Random Explorations

Quantifying space exploration is a central question in random walk theory, with direct applications ranging from animal foraging, diffusion-limited reactions, and intracellular transport to stock markets. In particular, the explored domain by one or many simple memoryless (or Markovian) random walks has received considerable attention . However, the physical systems mentioned above typically involve significant memory effects, and so far, no general framework exists to analyze such systems. We introduce the concept of a \emph{flip}, defined most naturally in one dimension, where the visited territory is $[x_{\rm min}, x_{\rm max}]$: a flip occurs when, after discovering a new site at $x_{\rm max}$, the walker next discovers $x_{\rm min} - 1$ instead of $x_{\rm max} + 1$ (and vice-versa). While it reduces to the classical splitting probability in Markovian systems, we show that the flip probability serves as a key observable for quantifying the impact of memory effects on space exploration. Here, we demonstrate that the flip probability follows a strikingly simple and universal law: it decays inversely with the number of sites visited, as $1/n$, independently of the underlying stochastic process. We confirm this behavior through simulations across paradigmatic non-Markovian models and observe it in real-world systems, without relying on model assumptions, including biological tracer motion, DNA sequences, and financial market dynamics. Finally, we reveal the physical mechanism behind this universality and show how it extends to higher-dimensional and fractal domains. Our determination of universal flip statistics lay the groundwork for understanding how memory effects govern random explorations.

cond-mat.stat-mech↗

arXiv2024

Persistence exponents of self-interacting random walks

The persistence exponent, which characterises the long-time decay of the survival probability of stochastic processes in the presence of an absorbing target, plays a key role in quantifying the dynamics of fluctuating systems. Determining this exponent for non-Markovian processes is known to be a difficult task, and exact results remain scarce despite sustained efforts. In this Letter, we consider the fundamental class of self-interacting random walks (SIRWs), which display long-range memory effects that result from the interaction of the random walker at time $t$ with the territory already visited at earlier times $t'<t$. We compute exactly the persistence exponent for all physically relevant SIRWs. As a byproduct, we also determine the splitting probability of these processes. Besides their intrinsic theoretical interest, these results provide a quantitative characterization of the exploration process of SIRWs, which are involved in fields as diverse as foraging theory, cell biology, and machine learning.

cond-mat.stat-mech↗

arXiv2024

Integer defects, flow localization, and bistability on curved active surfaces

Biological surfaces, such as developing epithelial tissues, exhibit in-plane polar or nematic order and can be strongly curved. Recently, integer (+1) topological defects have been identified as morphogenetic hotspots in living systems. Yet, while +1 defects in active matter on flat surfaces are well-understood, the general principles governing curved active defects remain unknown. Here, we study the dynamics of integer defects in an extensile or contractile polar fluid on two types of morphogenetically-relevant substrates : (1) a cylinder terminated by a spherical cap, and (2) a bump on an otherwise flat surface. Because the Frank elastic energy on a curved surface generically induces a coupling to $\textit{deviatoric}$ curvature, $\mathcal{D}$ (difference between squared principal curvatures), a +1 defect is induced on both surface types. We find that $\mathcal{D}$ leads to surprising effects including localization of orientation gradients and active flows, and particularly for contractility, to hysteresis and bistability between quiescent and flowing defect states.

cond-mat.soft↗

arXiv2024

Exact propagators of one-dimensional self-interacting random walks

Self-interacting random walks (SIRWs) show long-range memory effects that result from the interaction of the random walker at time $t$ with the territory already visited at earlier times $t'<t$. This class of non-Markovian random walks has applications in contexts as diverse as foraging theory, the behaviour of living cells, and even machine learning. Despite this importance and numerous theoretical efforts, the propagator, which is the distribution of the walker's position and arguably the most fundamental quantity to characterize the process, has so far remained out of reach for all but a single class of SIRW. Here we fill this gap and provide an exact and explicit expression for the propagator of two important classes of SIRWs, namely, the once-reinforced random walk and the polynomially self-repelling walk. These results give access to key observables, such as the diffusion coefficient, which so far had not been determined. We also uncover an inherently non-Markovian mechanism that tends to drive the walker away from its starting point.

cond-mat.stat-mech↗

arXiv2024

Target search kinetics for random walkers with memory

In this chapter, we consider the problem of a non-Markovian random walker (displaying memory effects) searching for a target. We review an approach that links the first passage statistics to the properties of trajectories followed by the random walker in the future of the first passage time. This approach holds in one and higher spatial dimensions, when the dynamics in the vicinity of the target is Gaussian, and it is applied to three paradigmatic target search problems: the search for a target in confinement, the search for a rarely reached configuration (rare event kinetics), or the search for a target in infinite space, for processes featuring stationary increments or transient aging. The theory gives access to the mean first passage time (when it exists) or to the behavior of the survival probability at long times, and agrees with the available exact results obtained perturbatively for examples of weakly non-Markovian processes. This general approach reveals that the characterization of the non-equilibrium state of the system at the instant of first passage is key to derive first-passage kinetics, and provides a new methodology, via the analysis of trajectories after the first-passage, to make it quantitative.

cond-mat.stat-mech↗

arXiv2023

Extreme Value Statistics of Jump Processes

We investigate extreme value statistics (EVS) of general discrete time and continuous space symmetric jump processes. We first show that for unbounded jump processes, the semi-infinite propagator $G_0(x,n)$, defined as the probability for a particle issued from $0$ to be at position $x$ after $n$ steps whilst staying positive, is the key ingredient needed to derive a variety of joint distributions of extremes and times at which they are reached. Along with exact expressions, we extract novel universal asymptotic behaviors of such quantities. For bounded, semi-infinite jump processes killed upon first crossing of zero, we introduce the \textit{strip probability} $μ_{0,\underline{x}}(n)$, defined as the probability that a particle issued from 0 remains positive and reaches its maximum $x$ on its $n^{\rm th}$ step exactly. We show that $μ_{0,\underline{x}}(n)$ is the essential building block to address EVS of semi-infinite jump processes, and obtain exact expressions and universal asymptotic behaviors of various joint distributions.

cond-mat.stat-mech↗

arXiv2022

Leftward, Rightward and Complete Exit Time Distributions of Jump Processes

First-passage properties of continuous stochastic processes confined in a 1--dimensional interval are well described. However, for jump processes (discrete random walks), the characterization of the corresponding observables remains elusive, despite their relevance in various contexts. Here we derive exact asymptotic expressions for the leftward, rightward and complete exit time distributions from the interval $[0,x]$ for symmetric jump processes starting from $x_0=0$, in the large $x$ and large time limit. We show that both the leftward probability $F_{\underline{0},x}(n)$ to exit through $0$ at step $n$ and rightward probability $F_{0,\underline{x}}(n)$ to exit through $x$ at step $n$ exhibit a universal behavior dictated by the large distance decay of the jump distribution parameterized by the Levy exponent $μ$. In particular, we exhaustively describe the $n\ll x^μ$ and $n\gg x^μ$ limits and obtain explicit results in both regimes. Our results finally provide exact asymptotics for exit time distributions of jump processes in regimes where continuous limits do not apply.

cond-mat.stat-mech↗

arXiv2022

Splitting Probabilities of Jump Processes

We derive a universal, exact asymptotic form of the splitting probability for symmetric continuous jump processes, which quantifies the probability $ π_{0,\underline{x}}(x_0)$ that the process crosses $x$ before 0 starting from a given position $x_0\in[0,x]$ in the regime $x_0\ll x$. This analysis provides in particular a fully explicit determination of the transmission probability ($x_0=0$), in striking contrast with the trivial prediction $ π_{0,\underline{x}}(0)=0$ obtained by taking the continuous limit of the process, which reveals the importance of the microscopic properties of the dynamics. These results are illustrated with paradigmatic models of jump processes with applications to light scattering in heterogeneous media in realistic 3$d$ slab geometries. In this context, our explicit predictions of the transmission probability, which can be directly measured experimentally, provide a quantitative characterization of the effective random process describing light scattering in the medium.

cond-mat.stat-mech↗

arXiv2022

Intermittent Attractive Interactions Lead to Microphase Separation in Non-motile Active Matter

Non-motile active matter exhibits a wide range of non-equilibrium collective phenomena yet examples are crucially lacking in the literature. We present a microscopic model inspired by the bacteria {\it Neisseria Meningitidis} in which diffusive agents feel intermittent attractive forces. Through a formal coarse-graining procedure, we show that this truly scalar model of active matter exhibits the time-reversal-symmetry breaking terms defining the {\it Active Model B+} class. In particular, we confirm the presence of microphase separation by solving the kinetic equations numerically. We show that the switching rate controlling the interactions provides a regulation mechanism tuning the typical cluster size, e.g. in populations of bacteria interacting via type IV pili.

cond-mat.soft↗

arXiv2021

Universal kinetics of imperfect reactions in confinement

Chemical reactions generically require that particles come into contact. In practice, reaction is often imperfect and can necessitate multiple random encounters between reactants. In confined geometries, despite notable recent advances, there is to date no general analytical treatment of such imperfect transport-limited reaction kinetics. Here, we determine the kinetics of imperfect reactions in confining domains for any diffusive or anomalously diffusive Markovian transport process, and for different models of imperfect reactivity. We show that the full distribution of reaction times is obtained in the large confining volume limit from the knowledge of the mean reaction time only, which we determine explicitly. This distribution for imperfect reactions is found to be identical to that of perfect reactions upon an appropriate rescaling of parameters, which highlights the robustness of our results. Strikingly, this holds true even in the regime of low reactivity where the mean reaction time is independent of the transport process, and can lead to large fluctuations of the reaction time even in simple reaction schemes. We illustrate our results for normal diffusion in domains of generic shape, and for anomalous diffusion in complex environments, where our predictions are confirmed by numerical simulations.

cond-mat.stat-mech↗

arXiv2021

Reply to Comment on "Inverse Square Lévy Walks are not Optimal Search Strategies for d \geq 2 "

We refute here the concernes raised in the Comment of our letter. This reply states clearly the validity range of our results and shows that the optimality of inverse-square Levy walks at the basis of the Levy flight foraging hypothesis is generically unfounded. We also give the precise set of conditions for which inverse-levy square Levy walks turn to be optimal, conditions which are unlikely to be verified biologically.

cond-mat.stat-mech↗

arXiv2020

Clustering and ordering in cell assemblies with generic asymmetric aligning interactions

Collective cell migration plays an essential role in various biological processes, such as development or cancer proliferation. While cell-cell interactions are clearly key determinants of collective cell migration -- in addition to individual cells self-propulsion -- the physical mechanisms that control the emergence of cell clustering and collective cell migration are still poorly understood. In particular, observations have shown that binary cell-cell collisions generally lead to anti-alignement of cell polarities and separation of pairs -- a process called contact inhibition of locomotion (CIL), which is expected to disfavor the formation of large scale cell clusters with coherent motion. Here, we adopt a joint experimental and theoretical approach to determine the large scale dynamics of cell assemblies from elementary pairwise cell-cell interaction rules. We quantify experimentally binary cell-cell interactions and show that they can be captured by a minimal equilibrium-like pairwise asymmetric aligning interaction potential that reproduces the CIL phenomenology. We identify its symmetry class, build the corresponding active hydrodynamic theory and show on general grounds that such asymmetric aligning interaction destroys large scale clustering and ordering, leading instead to a liquid-like microphase of cell clusters of finite size and short lived polarity, or to a fully dispersed isotropic phase. Finally, this shows that CIL-like asymmetric interactions in cellular systems -- or general active systems -- control cluster sizes and polarity, and can prevent large scale coarsening and long range polarity, except in the singular regime of dense confluent systems.

physics.bio-ph↗

arXiv2020

Kinetics of rare events for non-Markovian stationary processes and application to polymer dynamics

How much time does it take for a fluctuating system, such as a polymer chain, to reach a target configuration that is rarely visited -- typically because of a high energy cost ? This question generally amounts to the determination of the first-passage time statistics to a target zone in phase space with lower occupation probability. Here, we present an analytical method to determine the mean first-passage time of a generic non-Markovian random walker to a rarely visited threshold, which goes beyond existing weak-noise theories. We apply our method to polymer systems, to determine (i) the first time for a flexible polymer to reach a large extension, and (ii) the first closure time of a stiff inextensible wormlike chain. Our results are in excellent agreement with numerical simulations and provide explicit asymptotic laws for the mean first-passage times to rarely visited configurations.

cond-mat.stat-mech↗