Bias- and bath-meadited clustering of driven particles through a quiescent bath

When a particle is driven by an external force field through a quiescent bath it creates a non-equilibrium inhomogeneity in the surrounding bath. In this thesis we study the case with one driven particle and with more than one, in this case we will analyze the interaction between this driven particles on a two dimensional lattice. Such driven particle can be a charge carrier subject to an electric field or a colloid moved with an optical tweezer [12]. The bath particles may be seen as colloids dispersed in a solvent. These microstructural changes induced by the external driving have been observed experimentally, in particular in micro-rheological measurements of the drag force on a single colloid driven through a λ − DNA solution or for a biased motion of an intruder dragged into a monolayer of vi- brated grains [4] . The aim of this thesis is to characterize, through exhaustive numerical and an appropriate theory, the response of a system when two or more intruders are present. We want to characterize the dependence of the variance of the intruder's displacement as a function of the total number of driven particles in quasi one-dimensional systems and thus, gain infor- mation about the non-equilibrium induced correlations among different particles. For two driven particles it has been shown that such correlations induce an attractive interaction yielding the formation of pairs. Here we characterize the effective induced force between two driven particles and extend such characterization to study the statistics of clusters formation when the number of intruders is larger, namely the size distribution and its fluctuations. We show that the bias- and bath-mediated interaction leads to the formation of clusters. Furthermore, in the presence of confinement clogging appears.