Manuscript Em03-F@1 · Em03-F-v1.tex · section · 0d4d148b

Identical number statistics for opposite labels

Phase-sensitive witnesses and what number counts miss › Identical number statistics for opposite labels · lines 1201–1220

The two labels have identical count laws, but those laws need not equal the undisplaced Hawking baseline.

If $B = σ (k_{F}, l) \neq = 0$ , then for fixed profiles and witness,

ω_{s} (N_{h}) - ν_{h} = g^{2} ∣ c_{h} ∣^{2}, Δ_{s i n} = e^{- ∥ l ∥_{U}^{2} /2} ∣ B ∣ ∣ g ∣ + O (∣ g ∣^{3}) .

For $∣ g B ∣ \leq π /2$ ,

Δ_{s i n} \geq \frac{2}{π} e^{- ∥ l ∥_{U}^{2} /2} ∣ g B ∣.

Thus a phase-sensitive bounded witness can be first order while the occupation-mean departure is second order.

Displayed formulas in this passage

unlabeled · line 1207
$ω_{s} (N_{h}) - ν_{h} = g^{2} ∣ c_{h} ∣^{2}, Δ_{s i n} = e^{- ∥ l ∥_{U}^{2} /2} ∣ B ∣ ∣ g ∣ + O (∣ g ∣^{3}) .$
unlabeled · line 1213
$Δ_{s i n} \geq \frac{2}{π} e^{- ∥ l ∥_{U}^{2} /2} ∣ g B ∣.$