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

TL;DR

This paper investigates the fluctuations of a charged particle's orbital motion in crossed magnetic and electric fields using Langevin dynamics, revealing novel Hall and diamagnetic fluctuation effects.

Contribution

It introduces new fluctuation relations, including a transverse Hall fluctuation, and analyzes magnetic moment distributions under harmonic confinement.

Findings

Discovery of a transverse Hall fluctuation relation involving electric and magnetic fields.

Calculation of non-zero even moments of orbital magnetic moment not obtainable from classical free energy.

Identification of fluctuation effects in charged particle dynamics under crossed fields.

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.