Kramers equation for a charged Brownian particle: The exact solution

Simões, Tania P.; Lagos, Roberto E.

doi:10.1016/j.physa.2005.03.034

Cited by 34 publications

(25 citation statements)

References 12 publications

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“…We present our result, as in Ref. [77], in terms of the stream velocity u(x, t), in turn expressed as a magnetocovariant derivative…”

Section: Hydrothermodynamics Of Brownian Motionmentioning

confidence: 86%

“…We have extended our previous work on charged Brownian particles [73,75,77], in order to obtain a consistent expansion scheme in powers of the collision time. We presented the complete hydrothermodynamical picture for charged Brownian particles in the Kramers equation scheme, considering the action of external magnetic, electric and mechanical fields, chemical transformations within the BGK scheme, and furthermore space dependent thermal fields (inhomogeneous media).…”

Section: Discussionmentioning

confidence: 99%

“…Our results are equivalent to the asymptotic regime for an exact solution [77]: the local equilibrium approximation [131][132][133][134][135] is not fulfilled [136]; in particular the entropy density and the chemical potential are given, respectively by the expressions…”

Section: Applicationsmentioning

confidence: 96%

“…In his celebrated 1943 Brownian motion paper [11], Chandrasekhar outlined the method for solving a Brownian particle in a general field of force. It took approximately sixty years to report exact solutions for the Brownian motion of a charged particle in uniform and static electric and/or magnetic fields [71][72][73][74][75][76][77][78][79][80][81][82][83][84][85] (see also some previous related works [86,87]). …”

Section: Introductionmentioning

confidence: 99%

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

Lagos

Simões

2011

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tWe 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 Maxwell-Cattaneo-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.

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“…We present our result, as in Ref. [77], in terms of the stream velocity u(x, t), in turn expressed as a magnetocovariant derivative…”

Section: Hydrothermodynamics Of Brownian Motionmentioning

confidence: 86%

Section: Discussionmentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Lagos

Simões

2011

Physica A: Statistical Mechanics and its Applications

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“…The position r = (x,y) of a charged Brownian particle of mass m and charge q, confined to the x-y plane, and subject to an inhomogeneous magnetic field B = B(r)ẑ, evolves in time according to the Langevin equations [21] (1) is also a radial function,…”

Section: Modelmentioning

confidence: 99%

Anomalous cross-field diffusion in a magnetic trap

Savel’ev

Marchesoni

2014

Phys. Rev. E

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We numerically simulated the diffusion of a charged Brownian particle confined to a plane under the action of an orthogonal magnetic field with intensity depending on the distance from a center. Despite its apparent simplicity, this system exhibits anomalous diffusion. For positive field gradients, radial and angular dynamics are asymptotically subdiffusive, with exponents given by simple analytical expressions. In contrast, when driven by a weakly decaying field, the particle attains normal diffusion only after exceedingly long superdiffusive transients. These mechanisms can be related to Bohm diffusion in magnetized plasmas.

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Classical and quantum Brownian motion in an electromagnetic field

Patriarca

Sodano

2016

Fortschritte der Physik

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The dynamics of a Brownian particle in a constant magnetic field and time‐dependent electric field is studied in the limit of white noise, using a Langevin approach for the classical problem and the path‐integral Feynman‐Vernon and Caldeira‐Leggett framework for the quantum problem. A first goal of this study is to use the two‐dimensional problem of a Brownian particle in a magnetic field to show that a proper re‐formulation of the oscillator model of quantum Brownian motion allows one to recover the classical limit of the dynamics correctly. Furthermore, the probability distribution in configuration space of an initial pure state represented by an asymmetrical Gaussian wave function is worked out and its general time evolution is decomposed in the superposition of basic processes: (a) the classical motion of the center of mass, (b) a rotation around the mean position, and (c) spreading processes along the principal axes.

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Kramers equation for a charged Brownian particle: The exact solution

Cited by 34 publications

References 12 publications

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

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

Anomalous cross-field diffusion in a magnetic trap

Classical and quantum Brownian motion in an electromagnetic field

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