Langevin dynamics in crossed magnetic and electric fields: Hall and diamagnetic fluctuations

Abstract

Based on the classical Langevin equation, we have re-visited the problem of orbital motion of a charged particle in two dimensions for a normal magnetic field crossed with or without an in-plane electric bias. We are led to two interesting fluctuation effects: First, we obtain not only a longitudinal "work-fluctuation" relation as expected for a barotropic type system, but also a transverse work-fluctuation relation perpendicular to the electric bias. This "Hall fluctuation" involves the product of the electric and the magnetic fields. And second, for the case of harmonic confinement without bias, the calculated probability density for the orbital magnetic moment gives non-zero even moments, not derivable as field derivatives of the classical free energy.

arXiv comment4 pages, 2 figures, revised version

References in corpus (5)

• A nonequilibrium equality for free energy differences
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• The unreasonable effectiveness of equilibrium-like theory for interpreting non-equilibrium experiments
• A charged particle in a magnetic field - Jarzynski Equality
• Reexamination of experimental tests of the fluctuation theorem

Cited by in corpus (6)

• Brownian Dynamics of charged particles in a constant magnetic field
• Extracting work from a single heat bath - A case study on Brownian particle under external magnetic field in presence of information
• Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise
• Charged Brownian Particles: Kramers and Smoluchowski Equations and the Hydrothermodynamical Picture
• Work Relations Connecting Nonequilibrium Steady States Without Detailed Balance
• Nonequilibrium fluctuation theorems in the presence of a time-reversal symmetry-breaking field and nonconservative forces