= Three-point density correlation of an ideal quantum gas
{title2=$C^{(3)}=n_1n_2n_3+\epsilon\sum_{\rm cyclic}n_1|g_{23}|^2+2\operatorname{Re}(g_{12}g_{23}g_{31})$}
For a number-conserving Gaussian pairing state, six <permutations> give this expression. Each <transposition> has sign $\epsilon$, positive for <bosons> and negative for <fermions>; the two three-cycles have positive sign for either statistics. Equivalently it is the permanent or <determinant> of the three-by-three <one-body density matrix>. For bosonic <number states>, repeated-mode <factorial> corrections must be included instead of assuming that <Wick theorem>.
Back to article page
