Brownian Motion in a Magnetic Field

We investigate a motion of a colloid in a harmonic trap driven out of equilibrium by an external non-conservative force producing a torque in the presence of a uniform magnetic field. We find that steady state exists only for a proper range of parameters such as mass, viscosity coefficient, and stiffness of the harmonic potential, and the magnetic field, which is not observed in the overdamped limit. We derive the existence condition for the steady state. We examine the combined influence of the non-conservative force and the magnetic field on non-equilibrium characteristics such as non-Boltzmann steady-state probability distribution function, probability currents, entropy production, position-velocity correlation, and violation of fluctuation-dissipation relation.

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“…The equal-time correlation functions are found from U −1 ss in Eq. (25). For the isotropic case, rotational symmetry yields…”

Section: Two-time Correlation Functionsmentioning

confidence: 99%

Nonequilibrium driven by an external torque in the presence of a magnetic field

Lee

Kwon

2019

Phys. Rev. E

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“…The study of the Brownian motion of a charged particle in uniform and magnetostatic fields is of great importance in the description of the diffusion and transport of plasmas and heavy ions [1,2,3,4,5,6,7,8,9]. In these references the respective authors modeled the dynamics of the charged particle through the use of a Langevin equation [10] of the form…”

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confidence: 99%

Brownian motion of a charged particle driven internally by correlated noise

2008

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We give an exact solution to the generalized Langevin equation of motion of a charged Brownian particle in a uniform magnetic field that is driven internally by an exponentially correlated stochastic force. A strong dissipation regime is described in which the ensemble-averaged fluctuations of the velocity exhibit transient oscillations that arise from memory effects. Also, we calculate generalized diffusion coefficients describing the transport of these particles and briefly discuss how they are affected by the magnetic field strength and correlation time. Our asymptotic results are extended to the general case of internal driving by correlated Gaussian stochastic forces with finite autocorrelation times.

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“…There is a long history to the study of Brownian motion in a magnetic field for a classical, charged particle [32][33][34][35]. The early studies were based on the Langevin model in which the velocity drag coefficient γ is time-independent, and two mutually-perpendicular, fluctuating forces, act on a charge that circulates around a magnetic field.…”

Section: Magnetized Behaviormentioning

confidence: 99%

Two-dimensional chaotic thermostat and behavior of a thermalized charge in a weak magnetic field

Morales

2019

Phys. Rev. E

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A two-dimensional (2D) version of a chaotic thermostat is investigated. Its structure follows the concept previously introduced by the author to generate a one-dimensional chaotic thermostat, namely the usual friction force of a deterministic thermostat is supplemented with a self-consistent fluctuating force that depends on the drag coefficient associated with coupling to the heat bath. Azimuthal symmetry requires the thermostat to have two internal degrees of freedom, thus the Martyna-Klein-Tuckerman (MKT) model is chosen for the heat bath. The unmagnetized system exhibits two-dimensional diffusive behavior, achieves symmetric Maxwellian velocity distributions in the absence of an external potential, and satisfies the Einstein relation when an external force is applied. The velocity fluctuations display the characteristic exponential frequency spectrum associated with chaotic systems. The model is used to explore the diffusive motion of a thermalized charge in a weak magnetic field and the associated Hall and Pedersen mobilities. Over a range of magnetic field strengths the charge exhibits absolute negative mobility (ANM).

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Brownian Motion in a Magnetic Field

Cited by 31 publications

References 5 publications

Nonequilibrium driven by an external torque in the presence of a magnetic field

Nonequilibrium driven by an external torque in the presence of a magnetic field

Brownian motion of a charged particle driven internally by correlated noise

Two-dimensional chaotic thermostat and behavior of a thermalized charge in a weak magnetic field

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