Fluctuations and correlations of a driven tracer in a hard-core lattice gas

Abstract

We consider a driven tracer particle (TP) in a bath of hard-core particles undergoing continuous exchanges with a reservoir. We develop an analytical framework which allows us to go beyond the standard force-velocity relation used for this minimal model of active microrheology and quantitatively analyze, for any density of the bath particles, the fluctuations of the TP position and their correlations with the occupation number of the bath particles. We obtain an exact Einstein-type relation which links these fluctuations in the absence of a driving force and the bath particles density profiles in the linear driving regime. For the one-dimensional case we also provide an approximate but very accurate explicit expression for the variance of the TP position and show that it can be a non-monotoneous function of the bath particles density: counter-intuitively, an increase of the density may increase the dispersion of the TP position. We show that this non trivial behavior, which could in principle be observed in active microrheology experiments, is induced by subtle cross-correlations quantified by our approach.

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• Driven tracers in narrow channels
• Mean-field microrheology of a very soft colloidal suspension: inertia induces shear-thickening
• Motion of active tracer in a lattice gas with cross-shaped particles
• Distribution of the position of a driven tracer in a hardcore lattice gas
• Interactions enhance dispersion in fluctuating channels via emergent flows
• Finite-density effects in the Fredrickson-Andersen and Kob-Andersen kinetically-constrained models
• Many-body effects in tracer particle diffusion with applications for single-protein dynamics on DNA
• Universal scale-free decay of tracer-bath correlations in $d$-dimensional interacting particle systems