Brownian motion in a magnetic field

Czopnik, R.; Garbaczewski, Piotr

doi:10.1103/physreve.63.021105

Cited by 73 publications

(77 citation statements)

References 14 publications

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“…That becomes even more conspicuous in case of the Brownian motion of a charged particle in the constant magnetic field, [15,8,23]. In the Smoluchowski (large friction) regime, friction completely smoothes out any rotational (due to the Lorentz force) features of the process.…”

Section: Hydrodynamical Formalism For Random Dynamicsmentioning

confidence: 99%

“…As a specific example we shall discuss the dynamics of a charged particle in a constant magnetic field, see e.g. also [15,23,29,30].…”

Section: Kramers Equation and Local Conservation Lawsmentioning

confidence: 99%

“…In the Smoluchowski (large friction) regime, friction completely smoothes out any rotational (due to the Lorentz force) features of the process. In the corresponding local momentum conservation law there is no volume force contribution at all and merely the "pressuretype" potential Q appears in a rescaled form, [15]:…”

Section: Hydrodynamical Formalism For Random Dynamicsmentioning

confidence: 99%

“…The stationary (time homogeneous) transition probability density for the diffusion process without friction in phase-space has the form (15) and is the fundamental solution to Kramers (Fokker-Planck type) equation (14). We are interested in passing to a hydrodynamical picture, following the traditional recipes [14,16].…”

Section: Kramers Equation and Local Conservation Lawsmentioning

confidence: 99%

“…Let us mention that, as reveals the hydrodynamical formalism of the Brownian motion, [14], Brownian particles "while being thermalized", show up a continual net absorption of heat/energy from the reservoir (that point is normally disregarded in view of the very short relaxation times): socalled kinetic temperature grows up to the actual temperature of the bath, in parallel with the mean kinetic energy of the Brownian particle, [11,15,6], c.f. also [16,17].…”

Section: Introductionmentioning

confidence: 99%

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Frictionless random dynamics: hydrodynamical formalism

Czopnik

Garbaczewski

2003

Physica A: Statistical Mechanics and its Applications

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We investigate an undamped random phase-space dynamics in deterministic external force fields (conservative and magnetic ones). By employing the hydrodynamical formalism for those stochastic processes we analyze microscopic kinetic-type "collision invariants" and their relationship to local conservation laws (moment equations) in the fully nonequlibrium context. We address an issue of the continual heat absorption (particles "energization") in the course of the process and its possible physical implementations. IntroductionThe major topic discussed in the present paper will be the frictionless random motion which is introduced in close affinity with second-order processes driven by white noise, [1,2]. In the course of motion an unrestricted "energization" of particles is possible, a phenomenon which has not received much attention in the literature, although appears to be set on convincing phenomenological grounds in specific (nontypical) physical surroundings, [3,4].A classic problem of an irreversible behaviour of a particle embedded in the large encompassing system, [5,6,7] pertains to the random evolution of tracer particles in a fluid (like e.g. those performing Brownian motion). In that case, a particle -bath coupling is expected to imply quick relaxation towards a stationary probability distribution (equilibrium Maxwellian for a given a priori temperature T of the surrounding fluid/bath) and thus making the system amenable to standard fluctuationdissipation theorems. The dissipation of randomly acquired energy back to the bath is here enforced by dynamical friction mechanisms, [8,9,10,7], although no balance between stochastic forcing (random *

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Section: Hydrodynamical Formalism For Random Dynamicsmentioning

confidence: 99%

“…As a specific example we shall discuss the dynamics of a charged particle in a constant magnetic field, see e.g. also [15,23,29,30].…”

Section: Kramers Equation and Local Conservation Lawsmentioning

confidence: 99%

Section: Hydrodynamical Formalism For Random Dynamicsmentioning

confidence: 99%

Section: Kramers Equation and Local Conservation Lawsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Frictionless random dynamics: hydrodynamical formalism

Czopnik

Garbaczewski

2003

Physica A: Statistical Mechanics and its Applications

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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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Fluctuations, Information, Gravity and the Quantum Potential

Carroll¹

2006

144

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We show how the quantum potential arises in various ways and trace its connection to quantum fluctuations and Fisher information along with its realization in terms of Weyl curvature. It represents a genuine quantization factor for certain classical systems as well as an expression for quantum matter in gravity theories of Weyl-Dirac type. Many of the facts and examples are extracted from the literature (with references cited) and we mainly provide connections and interpretation, with a few new observations. We deliberately avoid ontological and epistemological discussion and resort to a collection of contexts where the quantum potential plays a visibly significant role. In particular we sketch some recent results of F. and A. Shojai on Dirac-Weyl action and Bohmian mechanics which connects quantum mass to the Weyl geometry. Connections a la Santamato of the quantum potential with Weyl curvature arising from a stochastic geometry, are also indicated for the Schrödinger equation (SE) and Klein-Gordon (KG) equation. Quantum fluctuations and quantum geometry are linked with the quantum potential via Fisher information. Derivations of SE and KG from Nottale's scale relativity are sketched along with a variety of approaches to the KG equation. Finally connections of geometry and mass generation via Weyl-Dirac geometry with many cosmological implications are indicated, following M. Israelit and N. Rosen.

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Brownian motion in a magnetic field

Cited by 73 publications

References 14 publications

Frictionless random dynamics: hydrodynamical formalism

Frictionless random dynamics: hydrodynamical formalism

Classical and quantum Brownian motion in an electromagnetic field

Fluctuations, Information, Gravity and the Quantum Potential

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