TL;DR
This paper investigates a Brownian harmonic oscillator that dissipates energy through friction or electromagnetic radiation, driven by quantum fluctuations, revealing universal velocity fluctuations and deriving key equations.
Contribution
It introduces a comprehensive theoretical framework for Brownian emitters, including the effects of the Abraham-Lorentz force and universal velocity fluctuation results.
Findings
Half-width depends on peak frequency due to Abraham-Lorentz force
Root-mean-square velocity fluctuation is approximately 1/18 of the speed of light for a charged particle in vacuum at zero temperature
Derived Klein-Kramers and Smoluchowski equations for the system
Abstract
A Brownian harmonic oscillator, which dissipates energy either by friction or via emission of electromagnetic radiation, is considered. This Brownian emitter is driven by the surrounding thermo-quantum fluctuations, which are theoretically described by the fluctuation-dissipation theorem. It is shown how the AbrahamLorentz force leads to dependence of the half-width on the peak frequency of the oscillator amplitude spectral density. It is also found that for the case of a charged particle, moving in vacuum at zero temperature, its root-mean-square velocity fluctuation is a universal constant, equal to roughly 1/18 of the speed of light. The relevant Klein-Kramers and Smoluchowski equations are derived as well.
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