= Gaussian resonance broadening
{c}
{title2=$\mathcal R_\Gamma(\omega)=(\sqrt{2\pi}\Gamma)^{-1}e^{-\omega^2/(2\Gamma^2)}$}
For a perturbation with amplitude envelope $e^{-(t-t_0)^2/(2\tau^2)}$, the squared <Fourier transform> is proportional to $e^{-\omega^2\tau^2}$. Hence pulse-integrated transport weights orbital detuning with a normalized <Gaussian function> of width $\Gamma=(\sqrt2\tau)^{-1}$. A longer pulse selects a narrower band of <orbital resonances>. This spectral broadening does not by itself assume stochastic temporal forcing.
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