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

Global bounded perturbations and finite leakage domains

B4 extraction: explicit swaps and control certificates › Global bounded perturbations and finite leakage domains · lines 1318–1342

Em03-B@2#eq:globalcontrol

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Suppose the implemented interaction-picture generator is

H_{E} (t) = H_{E} (t) + n = 1 \sum^{K} Δ u_{n} (t) R_{n} + G_{E} (t) .

Here $G_{E} (t)$ is explicitly bounded and self-adjoint. One permitted leakage model takes it supported on

P_{J}^{c} \otimes I_{Q}, J \geq K,

with finite-dimensional matrix elements. This allows temporary occupation up to $J$ , rather than silently identifying the initial cutoff $K$ with the maximum populated level.

Put

I_{E} = \int_{0}^{T_{E}} (1 \leq n \leq K max ∣Δ u_{n} (t) ∣ + ∥ G_{E} (t) ∥) d t, ζ_{glob} = min {1, I_{E}} .

Displayed formulas in this passage

Em03-B@2#eq:globalcontrol · line 1335
$I_{E} = \int_{0}^{T_{E}} (1 \leq n \leq K max ∣Δ u_{n} (t) ∣ + ∥ G_{E} (t) ∥) d t, ζ_{glob} = min {1, I_{E}} .$
unlabeled · line 1321
$H_{E} (t) = H_{E} (t) + n = 1 \sum^{K} Δ u_{n} (t) R_{n} + G_{E} (t) .$
unlabeled · line 1327
$P_{J}^{c} \otimes I_{Q}, J \geq K,$

Global bounded perturbations and finite leakage domains

Displayed formulas in this passage

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