= Static structure factor
{title2=$S(\mathbf k)$}
{wiki}
The static structure factor is the spatial <Fourier transform> of an equal-time <two-point correlation function>, with normalization and any disconnected contribution specified. It describes how spatial fluctuations contribute at each transferred <wavevector>.
If the <dynamic structure factor> is defined using the same correlation and the Fourier factor $e^{i\omega t}$, then
$$
S(\mathbf q)=\int\frac{d\omega}{2\pi}\,S(\mathbf q,\omega).
$$
The integral sets the time separation to zero. Evaluating the dynamic spectrum only at zero frequency instead selects a different quantity and generally does not produce the equal-time structure factor. A scattering experiment integrated over energy transfer can measure the static quantity after the relevant kinematic and detector corrections. A narrow peak near an ordering wavevector indicates long spatial correlations; it is not by itself a direct measurement of their relaxation time.
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