The rich phenomenology of Brownian particles in nonlinear potential landscapes
1 Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, Martí i Franquès 1, 08028 Barcelona, Spain
2 Departament de Física Aplicada, Universitat Politèctica de Catalunya, Avda. Doctor Marañón 44, 08028 Barcelona, Spain
a e-mail: email@example.com
Revised: 9 August 2010
Published online: 1 October 2010
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.
© EDP Sciences, Springer-Verlag, 2010