Manuscript Em03-H@8 · Em03-H-v8.tex · proposition · 91e9e3bd

Proposition: Uniform departure interpolation

Quench leakage, best compression, and departure · lines 706–720 · proof included or linked

Em03-H@8#prop:departuregrid

∣ p_{m a x} (u) - p_{m a x} (v) ∣ \leq n ∣ u - v ∣.

A validated grid of covering radius $δ$ requires an additional allowance $n δ$ for a uniform-time claim.

Proof. For $F_{0} = V^{†} e^{- i u A_{0}} V$ , $∥ F_{0} ∥ \leq 1$ , $F ˙_{0} \leq n /2$ , and $\frac{d}{d u} (F_{0}^{†} F_{0}) \leq n$ . Apply the Rayleigh principle.

Displayed formulas in this passage

unlabeled · line 708
$∣ p_{m a x} (u) - p_{m a x} (v) ∣ \leq n ∣ u - v ∣.$

Nearby in this section

section: Quench leakage, best compression, and departure
theorem: Theorem: Leakage and best compression
section: Quench leakage, best compression, and departure
theorem: Theorem: Departure and short-time estimates
lemma: Lemma: Odd compression and reached transitions
section: Quench leakage, best compression, and departure