Universal Large Deviations for the Tagged Particle in Single-File Motion

Hegde, Chaitra; Sabhapandit, Sanjib; Dhar, Abhishek

doi:10.1103/physrevlett.113.120601

Cited by 56 publications

(99 citation statements)

References 34 publications

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“…The problem was later studied by many other authors (see e.g. [20,25,42,77]). For Brownian particles the diffusion coefficient is constant, D(ρ) = 1, and the mobility is a linear function of density, σ(ρ) = 2ρ.…”

Section: Brownian Particles With Hard-core Repulsionmentioning

confidence: 97%

Tagged Particle in Single-File Diffusion

2015

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Single-file diffusion is a one-dimensional interacting infinite-particle system in which the order of particles never changes. An intriguing feature of single-file diffusion is that the mean-square displacement of a tagged particle exhibits an anomalously slow sub-diffusive growth. We study the full statistics of the displacement using a macroscopic fluctuation theory. For the simplest single-file system of impenetrable Brownian particles we compute the large deviation function and provide an independent verification using an exact solution based on the microscopic dynamics. For an arbitrary single-file system, we apply perturbation techniques and derive an explicit formula for the variance in terms of the transport coefficients. The same method also allows us to compute the fourth cumulant of the tagged particle displacement for the symmetric exclusion process.

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Section: Brownian Particles With Hard-core Repulsionmentioning

confidence: 97%

Tagged Particle in Single-File Diffusion

2015

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“…Without any such potential, one has an SSEP with fixed (independent of space and time) hopping rates for the particles, which is an old problem [27] and has been intensively studied in the last few decades [28][29][30][31][32][33][34][35][36][37][38]. In the presence of a time-periodic potential, the hopping rates become explicit functions of time, which has not been explored much until recently [10,11,39].…”

Section: Introductionmentioning

confidence: 99%

Symmetric exclusion processes on a ring with moving defects

Chatterjee

Pradhan

2016

Phys. Rev. E

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We study symmetric simple exclusion processes (SSEP) on a ring in the presence of uniformly moving multiple defects or disorders -a generalization of the model proposed earlier [Phys. Rev. E 89, 022138 (2014)]. The defects move with uniform velocity and change the particle hopping rates locally. We explore the collective effects of the defects on the spatial structure and transport properties of the system. We also introduce an SSEP with ordered sequential (sitewise) update and elucidate the close connection with our model.

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“…In dimension d ≥ 2, tracer diffusion has been shown to remain normal, with a non trivial diffusion coefficient resulting from many-body interactions and well approximated by the Nakazato-Kitahara approach [21]. In a "single-file" geometry, where particles cannot bypass each other, the impact of EVIs is stronger and results in a subdiffusive behavior x 2 (t) ∝ t β with β = 1/2 [22][23][24][25][26][27]. In this context, determining the effect of EVIs on systems with geometrical constraints appears an important question which does not seem to have received much attention.…”

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confidence: 99%

Diffusion and Subdiffusion of Interacting Particles on Comblike Structures

et al. 2015

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We study the dynamics of a tracer particle (TP) on a comb lattice populated by randomly moving hard-core particles in the dense limit. We first consider the case where the TP is constrained to move on the backbone of the comb only, and, in the limit of high density of particles, we present exact analytical results for the cumulants of the TP position, showing a subdiffusive behavior ∼ t 3/4 . At longer times, a second regime is observed, where standard diffusion is recovered, with a surprising non analytical dependence of the diffusion coefficient on the particle density. When the TP is allowed to visit the teeth of the comb, based on a mean-field-like Continuous Time Random Walk description, we unveil a rich and complex scenario, with several successive subdiffusive regimes, resulting from the coupling between the inhomogeneous comb geometry and particle interactions. Remarkably, the presence of hard-core interactions speeds up the TP motion along the backbone of the structure in all regimes.Subdiffusive motion of tracer particles in crowded media, e.g. biological cells, is widespread. Among the possible microscopic scenarios leading to this sublinear growth with time of the mean square displacement (MSD), the existence of geometric constraints related to the complexity of the environment plays an important role [1,2]. In this context, the comb model (see Fig. 1), in which a single particle moves on a two-dimensional space with the constraint that steps in the x direction are only allowed when the y coordinate of the particle positions is zero, has attracted considerable attention because of its simplicity and ability to reproduce subdiffusive behaviors of disordered systems [3].Comb-like structures have indeed been introduced as a first step to model diffusion in more complicated fractal structures like percolation clusters, the backbone and teeth of the comb representing the quasilinear structure and dangling ends of percolation clusters [4]. The particle can spend a long time exploring a tooth, which results in a subdiffusive motion along the backbone with x 2 (t) ∝ t α with α = 1/2. Since, numerous results have been obtained for this model [5][6][7][8][9][10][11][12], including the determination of the occupation time statistics [13], of mean first-passage times between two nodes of a finite comb [14] or the case of fractional Brownian walks on comb-like structures [15].In parallel, the comb model has been invoked to account for transport in real systems like spiny dendrites [10], diffusion of cold atoms [16] and mainly diffusion in crowded media like cells [17]. However, all existing studies have focused on single-particle diffusion, and interactions between particles have up to now been completely left aside. As an elementary model for diffusion of particles under short-range repulsive forces, we consider here excluded-volume interactions (EVIs) and focus on their impact on tracer dynamics on comb-like structures.From a theoretical point of view, lattice systems of interacting particles represent a protot...

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Universal Large Deviations for the Tagged Particle in Single-File Motion

Cited by 56 publications

References 34 publications

Tagged Particle in Single-File Diffusion

Tagged Particle in Single-File Diffusion

Symmetric exclusion processes on a ring with moving defects

Diffusion and Subdiffusion of Interacting Particles on Comblike Structures

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