Manuscript Psy03-A@1 · Psy03-A.tex · section · b30eb6e9

Coherence converted to a node population

Exact coherence-sensitive pilots › Coherence converted to a node population · lines 1810–1835

Psy03-A@1#eq:nodecalibration

This is a small Hamiltonian-edge restoration example, not a pharmacological regrowth theorem.

For a calibrated rectangle

Ω \in [Ω_{-}, Ω_{+}], γ \in [0, γ_{+}], γ_{+} < 2 Ω_{-},

choose $T Ω_{+} < π$ and put

w_{-} = Ω_{-}^{2} - γ_{+}^{2} /4 .

Then

C_{P_{0}} (T) \geq \frac{1}{2} e^{- γ_{+} T /2} min {sin (T w_{-}), sin (T Ω_{+})} > 0.

The bound follows from $Ω/ ω_{d} \geq 1$ , the frequency interval, and the minimum of sine on a subinterval of $(0, π)$ .

Displayed formulas in this passage

unlabeled · line 1816
$Ω \in [Ω_{-}, Ω_{+}], γ \in [0, γ_{+}], γ_{+} < 2 Ω_{-},$
unlabeled · line 1822
$w_{-} = Ω_{-}^{2} - γ_{+}^{2} /4 .$
Psy03-A@1#eq:nodecalibration · line 1826
$C_{P_{0}} (T) \geq \frac{1}{2} e^{- γ_{+} T /2} min {sin (T w_{-}), sin (T Ω_{+})} > 0.$