Two-tag correlations and nonequilibrium fluctuation–response relation in ageing single-file diffusion

Ooshida, Takeshi; Otsuki, Michio

doi:10.1088/1361-648x/aad4cc

Cited by 8 publications

(7 citation statements)

References 92 publications

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“…Note that this relation holds in the opposite limit of a dilute (ρ → 0) SEP [40]. (iii) Our approach provides the time dependence of all cumulants of individual particles and the law of the distance between TPs (insets of Fig.…”

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confidence: 95%

Bath-mediated interactions between driven tracers in dense single files

Poncet

Bénichou

Démery

et al. 2019

Phys. Rev. Research

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Single-file transport, where particles cannot bypass each other, has been observed in various experimental setups. In such systems, the behaviour of a tracer particle (TP) is subdiffusive, which originates from strong correlations between particles. These correlations are especially marked when the TP is driven and leads to inhomogeneous density profiles. Determining the impact of this inhomogeneity when several TPs are driven in the system is a key question, related to the general issue of bath-mediated interactions, which are known to induce collective motion and lead to the formation of clusters or lanes in a variety of systems. Quantifying this collective behaviour, the emerging interactions and their dependence on the amplitude of forces driving the TPs, remains a challenging but largely unresolved issue. Here, considering dense single-file systems, we analytically determine the entire dynamics of the correlations and reveal out of equilibrium cooperativity and competition effects between driven TPs.The motion of particles in narrow channels in which particles cannot bypass each other is known as singlefile diffusion. Such systems have been studied in various experimental setups with zeolites [1, 2], micro- [3,4] and nano-channels [5], and simulations of carbon nanotubes [6]. Key features, on the theoretical side, involve the existence of a subdiffusive scaling for the mean position of a given particle [7,8], and strong correlations between particles [9].The basic phenomenology of the single-file transport is well-captured by the symmetric exclusion process (SEP). In this paradigmatic model of crowded equilibrium systems, particles perform symmetric random walks on a one dimensional lattice with the constraint of at most a single occupancy of each lattice site. Different facets of the SEP have been scrutinised (see Refs. [8,[10][11][12][13][14][15]), including several important extensions to out-of-equilibrium situations. In particular, the mean displacement [16], as well as all higher-order cumulants [17] of an unbiased tagged particle (TP) placed initially at the shock point of a step-like density profile have been determined. Moreover, for a SEP with a single biased TP (due to either an energy consumption or an external force), the mean displacement of the latter [18,19] and the higher-order cumulants in the dense limit [20] have been calculated, and shown to grow sublinearly as √ t. Here, the particles accumulate in front of the TP and are depleted behind it, which results in an inhomogeneous, non-stationary spatial distribution of particles.A general open question concerns situations when several biased TPs are introduced in an otherwise quiescent medium of bath particles. The TPs are then expected to entrain the bath particles in a directional motion, which brings the system out-of-equilibrium and gives rise to effective bath-mediated interactions (BMIs) between the TPs. Such BMIs potentially lead to self-organisation, as observed in systems as diverse as colloidal solutions [21][22][23][24][25][26][27...

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mentioning

confidence: 95%

Bath-mediated interactions between driven tracers in dense single files

Poncet

Bénichou

Démery

et al. 2019

Phys. Rev. Research

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“…The random walk of the tracer (blue) is biased. Note that, when p1 = p−1 = 1/2, this model is identical to the classical SEP. fourth cumulant, all cumulants and two-time correlation functions in the dilute limit [14,26] or to other single-file models [27,28] have recently been proposed.…”

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confidence: 99%

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

2021

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The Symmetric Exclusion Process (SEP), where particles hop on a 1D 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 quenchedhas a quantitative impact on the long-time properties of tracer diffusion. However, so far, all the studies in the quenched case focused on the low-density limit of the SEP. Here, we derive the cumulant generating function of the tracer position in the 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.

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“…This striking result was first obtained analytically by Harris [48] (see Refs. [49,50] for a review), and holds also for all the cumulants of X(t) [51,52] and in case of multiple TPs [53][54][55]. On crowded comb-like structures, the TP mean-squared displacement exhibits a variety of sub-diffusive transients and, in some cases, an ultimate subdiffusive behaviour [56].…”

Section: Introductionmentioning

confidence: 89%

Tracer diffusion on a crowded random Manhattan lattice

et al. 2020

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We study, by extensive numerical simulations, the dynamics of a hard-core tracer particle (TP) in presence of two competing types of disorder-frozen convection flows on a square random Manhattan lattice and a crowded dynamical environment formed by a lattice gas of mobile hard-core particles. The latter perform lattice random walks, constrained by a single-occupancy condition of each lattice site, and are either insensitive to random flows (model A) or choose the jump directions as dictated by the local directionality of bonds of the random Manhattan lattice (model B). We focus on the TP disorder-averaged mean-squared displacement, (which shows a super-diffusive behaviour ∼t 4/3 , t being time, in all the cases studied here), on higher moments of the TP displacement, and on the probability distribution of the TP position X along the x-axis, for which we unveil a previously unknown behaviour. Indeed, our analysis evidences that in absence of the lattice gas particles the latter probability distribution has a Gaussian central part ( ) -u exp 2 , where u=X/t 2/3 , and exhibits slower-than-Gaussian tails ( | | ) u exp 4 3 for sufficiently large t and u. Numerical data convincingly demonstrate that in presence of a crowded environment the central Gaussian part and non-Gaussian tails of the distribution persist for both models.

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Two-tag correlations and nonequilibrium fluctuation–response relation in ageing single-file diffusion

Cited by 8 publications

References 92 publications

Bath-mediated interactions between driven tracers in dense single files

Bath-mediated interactions between driven tracers in dense single files

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

Tracer diffusion on a crowded random Manhattan lattice

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