arXiv subjects

Aurélien Grabsch

Publications and source records attributed to Aurélien Grabsch.

At least 19 recordsLinked to original sources

arXiv2026

Transverse geometry reshapes current and tracer fluctuation amplitudes in quasi-one-dimensional single files

Single-file transport means no overtaking: particles move in a narrow channel while preserving their longitudinal order. This simple constraint has profound dynamical consequences, most notably tracer subdiffusion, and has made single-file transport a paradigmatic form of confined many-body motion, observed from molecular transport in zeolites to single-file diffusion of colloids in narrow channels. A common modelling approach assumes that, once overtaking is suppressed, finite-width effects can be discarded or represented by an effective particle size in a strictly one-dimensional model. Starting from the Brownian dynamics in the full confined geometry, we instead derive the exact large-scale one-dimensional fluctuating-hydrodynamic equation governing the coarse-grained line density. Its transport coefficients are fixed by the confined equilibrium equation of state, through which the transverse geometry remains encoded in the one-dimensional description. Consequently, transverse geometry leaves the $t^{1/2}$ single-file scaling unchanged but can qualitatively reshape the density dependence of the current and tracer fluctuation amplitudes. In the minimal hard-core setting, this yields a collective diffusivity that can become non-monotonic in density for sufficiently wide no-passing channels. This geometric non-monotonicity propagates to exact large-scale predictions for the amplitudes of integrated-current fluctuations and tracer-displacement fluctuations. The effect is robust to the interaction potential, channel geometry, initial preparation and microscopic dynamics. Quasi-one-dimensional single-file transport therefore defines a distinct regime in which forbidding overtaking does not erase geometry from collective transport.

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arXiv2026

Exact Nonlinear Active Microrheology in Diffusive Single-File Systems

Active microrheology probes a crowded medium by forcing a tracer and measuring its response. In single-file transport, where particles cannot overtake, a constant force $F$ produces a subballistic displacement $\langle X_t\rangle\simeq \sqrt{t}\,ξ(F)$ together with a persistent bath deformation. Despite decades of work, the exact nonlinear response at arbitrary force has remained confined to a few special solvable models. Here we remove this restriction by combining recent advances in hydrodynamic transport coefficients, a pressure-balance formulation of the local drive, and single-file duality, which eliminates the resulting moving boundary. This yields a closed exact boundary-value problem for general diffusive single files, determining both $ξ(F)$ and the full density profile. For overdamped Brownian particles with general interactions, all microscopic interaction details enter only through the equilibrium equation of state, bringing realistic interacting systems, including finite-width quasi-one-dimensional channels, within exact reach. The solution also reveals universal global laws; in particular, the bath-density dipole is fixed by the applied force independently of the interaction potential.

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arXiv2026

A shortcut through the macroscopic fluctuation theory: a generalised Fick law

The macroscopic fluctuation theory is a powerful tool to characterise the large scale dynamical properties of diffusive systems, both in- and out-of-equilibrium. It relies on an action formalism in which, at large scales, the dynamics is fully determined by the minimum of the action. Within this formalism, the analysis of the statistical properties of a given observable reduces to solving the Euler-Lagrange equations with the appropriate boundary conditions. One must then compute the action at its minimum to deduce the cumulant generating function of the observable. This typically involves computing multiple integrals of cumbersome expressions. Recently, a simple formula has been conjectured to shortcut this last step, and compute the cumulant generating function of different observables (integrated current or position of a tracer) without the need to compute any integral. In this work, we prove this simple formula, and extend it to more general observables. We then illustrate the efficiency of this approach by applying it to compute the variance of a generalised current in the semi-infinite symmetric exclusion process and the joint properties of two occupation times in any diffusive system. In the case of the integrated current, our formula can be interpreted as a generalisation of Fick's law to obtain all the cumulants of the current beyond the average value.

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arXiv2026

Macroscopic fluctuation theory of interacting Brownian particles

We apply the macroscopic fluctuation theory (MFT) to study the large-scale dynamical properties of Brownian particles with arbitrary pairwise interaction. By combining it with standard results of equilibrium statistical mechanics for the collective diffusion coefficient, the MFT gives access to the exact large-scale dynamical properties of the system, both in- and out-of-equilibrium. In particular, we obtain exact results for dynamical correlations between the density and the current of particles. For one-dimensional systems, this allows us to obtain a precise description of these correlations for emblematic models, such as the Calogero and Riesz gases, and for systems with nearest-neighbor interactions such as the Rouse chain of hardcore particles or the recently introduced model of tethered particles. Tracer diffusion with the single-file constraint (but for arbitrary pairwise interaction) is also studied. For higher-dimensional systems, we quantitatively characterize these dynamical correlations by relying on standard methods such as the virial expansion.

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arXiv2025

Exact large-scale correlations in diffusive systems with general interactions: explicit characterisation without the Dean--Kawasaki equation

Characterising the statistical properties of classical interacting particle systems is a long-standing question. For Brownian particles the microscopic density obeys a stochastic evolution equation, known as the Dean--Kawasaki equation. This equation remains mostly formal and linearization (or higher-order expansions) is required to obtain explicit expressions for physical observables, with a range of validity not easily defined. Here, by combining macroscopic fluctuation theory with equilibrium statistical mechanics, we provide a systematic alternative to the Dean--Kawasaki framework to characterize large-scale correlations. This approach enables us to obtain explicit and exact results for dynamical observables such as tracer cumulants and bath-tracer correlations in one dimension, both in and out of equilibrium. In particular, we reveal a generic non-monotonic spatial structure in the response of the bath following a temperature quench. Our approach applies to a broad class of interaction potentials and extends naturally to higher dimensions.

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arXiv2025

Universal scale-free decay of tracer-bath correlations in $d$-dimensional interacting particle systems

Quantifying the correlations between the position of a tagged tracer and the density of surrounding bath particles is crucial for understanding tracer diffusion in interacting particle systems, and for characterizing the response properties of the bath. We address this problem analytically for both hard-core and soft-core interactions, using minimal yet paradigmatic models in $d$ spatial dimensions. In both cases, we derive analytical expressions for the spatial correlation profiles in the reference frame of the tracer. We reveal unexpected universal features in their large-distance behavior, characterized by power-law tails with exponents that depend solely on the spatial dimensionality of the system. Beyond these simple models, we demonstrate the robustness of our results across different regimes using particle-based numerical simulations.

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arXiv2025

Tracer and current fluctuations in driven diffusive systems

Interacting particles diffusing in single-file is a fundamental model of transport in narrow channels where particles cannot bypass each other. An important result has been obtained by Kollmann [Phys. Rev. Lett. 90, 180602 (2003)] for the mean square displacement of a tracer for any single-file model. It applies to any diffusive system, in particular the notable classes of colloidal systems and diffusive stochastic lattice gases. Since then, no analog result has been obtained in the important case where the particles are driven by an external field. Here, we fill this gap and determine the fluctuations and the skewness of the tracer's position for any driven diffusive system. In addition, we also consider a variety of important observables such as the integrated current, the response of the system to the perturbation induced by the displacement of the tracer, and the correlations between several tracers. Furthermore, we also unveil fundamental relations underlying the out-of-equilibrium dynamics of driven diffusive systems. This work constitutes a step toward the determination of the full distribution of all these observables in driven one-dimensional systems of interacting particles.

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arXiv2025

Full stochastic dynamics of a tracer in a dense single-file system

Tracer diffusion in single-file systems, where particles are restricted to move on a line without passing each other, has been a fertile ground to investigate anomalous diffusion and strong memory effects. While the long-time behavior of such a tracer has been well studied, with a known subdiffusive dynamics and a Gaussian description for the rescaled position, the finer details of multi-time correlations remain poorly understood. This work focuses on the limit where almost all sites of a Symmetric Exclusion Process (SEP), a paradigmatic lattice model, are occupied. It extends beyond Gaussian descriptions and single-time statistics to address the multi-time correlation functions of the tracer in the SEP. In this dense limit, we present a general relation between all $n$-time correlations of the non-Markovian tracer position process and the conditional probabilities of a single Markovian random walker. Using this relation, we derive explicit expressions for the four-time correlations and further explore important extensions: multiple tracers, non-equilibrium situations, and finite observation times. Our results underscore significant memory effects, strong temporal correlations, and the influence of initial conditions on long-time dynamics.

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arXiv2025

Dynamics of soft interacting particles on a comb

We study the dynamics of overdamped Brownian particles interacting through soft pairwise potentials on a comb-like structure. Within the linearized Dean-Kawasaki framework, we characterize the particle density fluctuations by computing their one- and two-point correlation functions. For a tracer particle constrained to move along the comb backbone, we determine the spatial correlation profile between its position and the density of surrounding bath particles. Furthermore, we derive the correction to the diffusion coefficient of the tracer due to interactions with other particles, validating our results through numerical simulations.

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arXiv2024

Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry

The symmetric simple exclusion process (SEP) is a paradigmatic model of transport, both in and out-of-equilibrium. In this model, the study of currents and their fluctuations has attracted a lot of attention. In finite systems of arbitrary dimension, both the integrated current through a bond (or a fixed surface), and its fluctuations, grow linearly with time. Conversely, for infinite systems, the integrated current displays different behaviours with time, depending on the geometry of the lattice. For instance, in 1D the integrated current fluctuations are known to grow sublinearly with time, as $\sqrt{t}$. Here we study the fluctuations of the integrated current through a given lattice bond beyond the 1D case by considering a SEP on higher-dimensional lattices, and on a comb lattice which describes an intermediate situation between 1D and 2D. We show that the different behaviours of the current originate from qualitatively and quantitatively different current-density correlations in the systems, which we compute explicitly.

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arXiv2024

Semi-infinite simple exclusion process: from current fluctuations to target survival

The symmetric simple exclusion process (SEP), where diffusive particles cannot overtake each other, is a paradigmatic model of transport in the single-file geometry. In this model, the study of currents has attracted a lot of attention, but so far most results are restricted to two geometries: (i) a finite system between two reservoirs, which does not conserve the number of particles but reaches a nonequilibrium steady state, and (ii) an infinite system which conserves the number of particles but never reaches a steady state. Here, we determine the full cumulant generating function of the integrated current in the important intermediate situation of a semi-infinite system connected to a reservoir, which does not conserve the number of particles and never reaches a steady state. This result is obtained thanks to the determination of the full spatial structure of the correlations which remarkably obey the very same closed equation recently obtained in the infinite geometry. Besides their intrinsic interest, these results allow us to solve two open problems: the survival probability of a fixed target in the SEP, and the statistics of the number of particles injected by a localized source.

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arXiv2024

Tracer diffusion beyond Gaussian behavior: explicit results for general single-file systems

Single-file systems, in which particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined geometries, such as in zeolites or carbon nanotubes. Twenty years ago, the mean squared displacement of a tracer was determined at large times, for any diffusive single-file system. Since then, for a general single-file system, even the determination of the fourth cumulant, which probes the deviation from Gaussianity, has remained an open question. Here, we fill this gap and provide an explicit formula for the fourth cumulant of an arbitrary single-file system. Our approach also allows us to quantify the perturbation induced by the tracer on its environment, encoded in the correlation profiles. These explicit results constitute a first step towards obtaining a closed equation for the correlation profiles for arbitrary single-file systems.

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arXiv2024

From Particle Currents to Tracer Diffusion: Universal Correlation Profiles in Single-File Dynamics

Single-file transport refers to the motion of particles in a narrow channel, such that they cannot bypass each other. This constraint leads to strong correlations between the particles, described by correlation profiles, which measure the correlation between a generic observable and the density of particles at a given position and time. They have recently been shown to play a central role in single-file systems. Up to now, these correlations have only been determined for diffusive systems in the hydrodynamic limit. Here, we consider a model of reflecting point particles on the infinite line, with a general individual stochastic dynamics. We show that the correlation profiles take a simple universal form, at arbitrary time. We illustrate our approach by the study of the integrated current of particles through the origin, and apply our results to representative models such as Brownian particles, run-and-tumble particles and Lévy flights. We further emphasise the generality of our results by showing that they also apply beyond the 1d case, and to other observables.

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arXiv2024

Joint distribution of currents in the symmetric exclusion process

The symmetric simple exclusion process (SEP) is a paradigmatic model of diffusion in a single-file geometry, in which the particles cannot cross. In this model, the study of currents have attracted a lot of attention. In particular, the distribution of the integrated current through the origin, and more recently, of the integrated current through a moving reference point, have been obtained in the long time limit. This latter observable is particularly interesting, as it allows to obtain the distribution of the position of a tracer particle. However, up to now, these different observables have been considered independently. Here, we characterise the joint statistical properties of these currents, and their correlations with the density of particles. We show that the correlations satisfy closed integral equations, which generalise the ones obtained recently for a single observable. We also obtain boundary conditions verified by these correlations, which take a simple physical form for any single-file system. As a consequence of our results, we quantify the correlations between the displacement of a tracer, and the integrated current of particles through the origin.

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arXiv2023

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 behaviour 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.

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arXiv2023

Driven Tracer in the Symmetric Exclusion Process: Linear Response and Beyond

Tracer dynamics in the Symmetric Exclusion Process, where hardcore particles diffuse on an infinite one-dimensional lattice, is a paradigmatic model of anomalous diffusion. While the equilibrium situation has received a lot of attention, the case where the tracer is driven by an external force, which provides a minimal model of nonequilibrium transport in confined crowded environments, remains largely unexplored. Indeed, the only available analytical results concern the means of both the position of the tracer and the lattice occupation numbers in its frame of reference, and higher-order moments but only in the high-density limit. Here, we provide a general hydrodynamic framework that allows us to determine the first cumulants of the bath-tracer correlations and of the tracer's position in function of the driving force, up to quadratic order (beyond linear response). This result constitutes the first determination of the bias-dependence of the variance of a driven tracer in the SEP for an arbitrary density. The framework presented here can be applied, beyond the SEP, to more general configurations of a driven tracer in interaction with obstacles in one dimension.

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arXiv2023

Duality relations in single-file diffusion

Single-file transport, which corresponds to the diffusion of particles that cannot overtake each other in narrow channels, is an important topic in out-of-equilibrium statistical physics. Various microscopic models of single-file systems have been considered, such as the simple exclusion process, which has reached the status of a paradigmatic model. Several different models of single-file diffusion have been shown to be related by a duality relation, which holds either microscopically or only in the hydrodynamic limit of large time and large distances. Here, we show that, within the framework of fluctuating hydrodynamics, these relations are not specific to these models and that, in the hydrodynamic limit, every single-file system can be mapped onto a dual single-file system, which we characterise. This general duality relation allows us to obtain new results for different models, by exploiting the solutions that are available for their dual model.

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arXiv2022

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 (i) a biased tracer; (ii) comb-like structures; and (iii) $d$-dimensional situations.

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