Manuscript En01-C@1 · En01-C.tex · section · 00a2161c

Gaussian kernel and point-pair coherence

Gaussian preparation and outcome-conditioned splitting › Gaussian kernel and point-pair coherence · lines 1012–1031

En01-C@1#eq:kernel

Fourier inversion of the Gaussian Wigner function gives

ρ (x, y) = \frac{1}{2 π v _{x}} exp [- \frac{( x + y ) ^{2}}{8 v _{x}} - \frac{det V}{2 ℏ ^{2} v _{x}} (x - y)^{2} + \frac{i c}{2ℏ v _{x}} (x^{2} - y^{2})] .

Define

P = \frac{ℏ}{2 det V}, ξ = P 8 v_{x} .

These are purity and the reference Gaussian coherence length, respectively Pino2018.

Displayed formulas in this passage

En01-C@1#eq:kernel · line 1015
$ρ (x, y) = \frac{1}{2 π v _{x}} exp [- \frac{( x + y ) ^{2}}{8 v _{x}} - \frac{det V}{2 ℏ ^{2} v _{x}} (x - y)^{2} + \frac{i c}{2ℏ v _{x}} (x^{2} - y^{2})] .$
unlabeled · line 1024
$P = \frac{ℏ}{2 det V}, ξ = P 8 v_{x} .$