Bath-mediated interactions between driven tracers in dense single files

Abstract

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...

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

“…1). The mean position [19,20] and all higher-order moments in the dense limit [13] have been calculated, and shown to grow anomalously as √ t. Recent extensions of this model concern the case of several driven tracers [21] or of a finite system [22,23]. Note that a similar behaviour of the first two cumulants is found for a symmetric tracer in an inhomogeneous bath, namely a step of density [18].…”

Bodies in an Interacting Active Fluid: Far-Field Influence of a Single Body and Interaction Between Two Bodies

“…which differs by a factor of 1/2 from the well-established current-force relation (54). As discussed below, this apparent contradiction is resolved if one properly defines the area integral over the entire system appearing in Eq.…”

“…Here we address two different issues about how the infinite-size limit is achieved. First, we clarify the meaning of the infinite-area integral appearing in the current-force relation (54). Second, we briefly discuss how the finite-size effects modify the derivations shown in Sec.…”

“…C.1 Derivation of the current-force relation (54) Integrating Eq. ( 9) side by side over the entire space, we obtain…”

“…As discussed below, this apparent contradiction is resolved if one properly defines the area integral over the entire system appearing in Eq. (54).…”