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 Abraham–Lorentz force leads to dependence of the half-width on the peak frequency of the oscillator amplitude spectral density. It is 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 Fokker–Planck and Smoluchowski equations are also derived.
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