Manuscript Em03-B@2 · Em03-B-v2.tex · section · c1a0977d

Dynamics, switching, and the unitary model

B4 capture: an explicit passive input–output interaction › Dynamics, switching, and the unitary model · lines 981–993

Em03-B@2#eq:captcontrol

Fix a normalized $f = f_{L}$ , supported in $(a, b) = (- 2 L, 2 L)$ , and a capture transmissivity $0 < τ < 1$ . Set

D (t) = 1 - τ + τ \int_{a}^{t} ∣ f (s) ∣^{2} d s, λ (t) = \frac{τ f ( t )}{D ( t )}, κ (t) = ∣ λ (t) ∣^{2} .

Outside $[a, b]$ , the coupling is zero.

Displayed formulas in this passage

Em03-B@2#eq:captcontrol · line 985
$D (t) = 1 - τ + τ \int_{a}^{t} ∣ f (s) ∣^{2} d s, λ (t) = \frac{τ f ( t )}{D ( t )}, κ (t) = ∣ λ (t) ∣^{2} .$