The rich phenomenology of Brownian particles in nonlinear potential landscapes |
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Authors: | JM Sancho and AM Lacasta |
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Institution: | (1) Max Planck Institute for Polymer Research, Ackermannweg, 10, 55128, Mainz, Germany;(2) Chemical Engineering Department, University of Florida, Gainesville, FL, 32611-6005, USA |
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Abstract: | Non-interacting Brownian particles obey Langevin equations fulfilling a fluctuation–dissipation relation between friction
and thermal noise. Under a linear potential (constant force) Einstein found a relation between diffusion and transport through
mobility. In nonlinear potentials this prediction is only satisfied within the limits of very small and large constant external
forces. Moreover, other more interesting behaviors do appear, such as: dispersionless transport, sorting, giant diffusion,
subdiffusion, superdiffusion, subtransport, etc. All these phenomena depend on the characteristics of the nonlinear potential
landscape: periodic or random, the symmetries and boundary conditions. Moreover, the presence of transport is the keystone
of most of this phenomenology. In this review, we present numerical simulations illustrating these facts and theoretical analysis
when possible. |
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