Charged Brownian particles: Kramers and Smoluchowski equations and the hydrothermodynamical picture

• Autor(a) principal: Lagos, R. E. [UNESP]
• Data de Publicação: 2011
• Outros Autores: Simes, Tania P.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1016/j.physa.2010.12.032; http://hdl.handle.net/11449/72401
• topic: Brownian motion; Brownian motors; Carrier transport; Dissipative dynamics; Evolution of nonequilibrium systems; Kramers equation; Smoluchowski equation; Kramers equations; Distribution functions; Entropy; Variational techniques; Brownian movement

We consider a charged Brownian gas under the influence of external and non-uniform electric, magnetic and mechanical fields, immersed in a non-uniform bath temperature. With the collision time as an expansion parameter, we study the solution to the associated Kramers equation, including a linear reactive term. To the first order we obtain the asymptotic (overdamped) regime, governed by transport equations, namely: for the particle density, a Smoluchowski- reactive like equation; for the particle's momentum density, a generalized Ohm's-like equation; and for the particle's energy density, a MaxwellCattaneo-like equation. Defining a nonequilibrium temperature as the mean kinetic energy density, and introducing Boltzmann's entropy density via the one particle distribution function, we present a complete thermohydrodynamical picture for a charged Brownian gas. We probe the validity of the local equilibrium approximation, Onsager relations, variational principles associated to the entropy production, and apply our results to: carrier transport in semiconductors, hot carriers and Brownian motors. Finally, we outline a method to incorporate non-linear reactive kinetics and a mean field approach to interacting Brownian particles. © 2011 Elsevier B.V. All rights reserved.