Collective excitations in jammed states: ultrafast defect propagation and finite-size scaling

Abstract

In crowded systems, particle currents can be mediated by propagating collective excitations which are generated as rare events, are localized and have a finite lifetime. The theoretical description of such excitations is hampered by the problem of identifying complex many-particle transition states, calculation of their free energies, and the evaluation of propagation mechanisms and velocities. Here we show that these problems can be tackled for a highly jammed system of hard spheres in a periodic potential. We derive generation rates of collective excitations, their anomalously high velocities, explain the occurrence of an apparent jamming transition and its strong dependence on the system size. The particle currents follow a scaling behavior, where for small systems the current is proportional to the generation rate and for large systems given by the geometric mean of the generation rate and velocity. Our theoretical approach is widely applicable to dense nonequilibrium systems in confined geometries. It provides new perspectives for studying dynamics of collective excitations in experiments.

Overcrowding induces fast colloidal solitons in a slowly rotating potential landscape

“…As the potential barrier U 0 is much larger than k B T , formation and propagation of solitons can be understood by considering the limit of vanishing noise. Theoretically, the solitons consist of periodically repeating movements of clusters with different size in this limit 11 , 49 , for which the equations of motions in the corotating frame are Introducing scaled dimensionless coordinates and time, , t → λ 2 t /( π μ U 0 ), and a dimensionless driving force f = λ ω R /( π μ U 0 ) = F λ /( π U 0 ), these equations take the form Solving Eq. ( 4 ) subject to the force conditions ( 2 ) and an initial condition with one double-occupied potential well, we find that after a transient time, periodic motions of two soliton types appear as limit cycles: an A type soliton given by two subintervals of the movements of an n - and ( n + 1)-cluster during one period [ n -( n + 1)-soliton], and a B type soliton given by four subintervals of cluster movements [ n -( n + 1)-( n + 2)-( n + 1)-soliton].…”

Overcrowding induces fast colloidal solitons in a slowly rotating potential landscape

“…As the potential barrier U 0 is much larger than k B T , formation and propagation of solitons can be understood by considering the limit of vanishing noise. Theoretically, the solitons consist of periodically repeating movements of clusters with different size in this limit 45,46 , for which the equations of motions in the corotating frame are…”

Hydrodynamic interactions hinder transport of flow-driven colloidal particles

“…In the absence of HI, the currents increase with density at large ρ , which can be attributed to a cluster speed-up effects discussed in ref. 65–67.…”