= Fermi window
{title2=$w(\epsilon)=-\partial_\epsilon n_F=[4k_BT]^{-1}\operatorname{sech}^2[(\epsilon-\mu)/(2k_BT)]$}
The <Fermi window> measures sensitivity of occupation to <energy> near the <chemical potential>. It is positive, even about $\mu$, has width of order $k_BT$, and integrates to one over the full <energy> line. Its centred <variance> is $\pi^2(k_BT)^2/3$. A band restricted to nonnegative <energy> contains weight $n_F(0,\mu)$ instead of exactly one; extending to the full line is exponentially accurate when $\mu\gg k_BT$. At zero <temperature> the window tends to a <Dirac delta function> at the <chemical potential>.
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