= Vector noise normalization in inertial Langevin dynamics
{title2=$\langle\mathbf A(t)\cdot\mathbf A(s)\rangle=(6\gamma k_BT/m^2)\delta(t-s)$}
Divide the inertial <Langevin equation> by mass and let $\zeta=\gamma/m$. An isotropic three-dimensional equilibrium velocity has $\langle|\mathbf u|^2\rangle=3k_BT/m$ by the <equipartition theorem>. Its white acceleration dot-covariance amplitude is therefore $6\zeta k_BT/m$, while the amplitude per Cartesian component is $2\zeta k_BT/m$. A scalar moment formula must use the component variance rather than the trace.
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