Solitary cluster waves in periodic potentials: Formation, propagation, and soliton-mediated particle transport

Abstract

Transport processes in crowded periodic structures are often mediated by cooperative movements of particles forming clusters. Recent theoretical and experimental studies of driven Brownian motion of hard spheres showed that cluster-mediated transport in one-dimensional periodic potentials can proceed in form of solitary waves. We here give a comprehensive description of these solitons. Fundamental for our analysis is a static presoliton state, which is formed by a periodic arrangement of basic stable clusters. Their size follows from a geometric principle of minimum free space. Adding one particle to the presoliton state gives rise to solitons. We derive the minimal number of particles needed for soliton formation, number of solitons at larger particle numbers, soliton velocities and soliton-mediated particle currents. Incomplete relaxations of the basic clusters are responsible for an effective repulsive soliton-soliton interaction seen in measurements. A dynamical phase transition is predicted to occur in current-density relations at low temperatures. Our results provide a theoretical basis for describing experiments on cluster-mediated particle transport in periodic potentials.

21 pages, 12 figures

References in corpus (5)

• Classical dynamical density functional theory: from fundamentals to applications
• Power functional theory for many-body dynamics
• Collective Directional Locking of Colloidal Monolayers on a Periodic Substrate
• Solitons in overdamped Brownian dynamics
• Brownian dynamics simulations of hard rods in external fields and with contact interactions

Cited by in corpus (4)

• Phase locking and fractional Shapiro steps in collective dynamics of microparticles
• Fast Brownian cluster dynamics
• Correlations of density and current fluctuations in single-file motion of hard spheres and in driven lattice gas with nearest-neighbor interaction
• Nonequilibrium phase transition in single-file transport at high crowding