Manuscript Hawk02-C@2 · Hawk02-C.tex · section · bb332d66

Perturbations on the checked invariant sector

Perturbations on the checked invariant sector · lines 1337–1371

Hawk02-C@2#eq:Eblock

The field interaction is unbounded on full Fock space. The following comparison is made on its specified one-excitation sector.

Let $E_{1} (t)$ be bounded, Hermitian, strongly measurable, and satisfy

\int_{0}^{T} ∥ E_{1} (t) ∥_{\infty} d t < \infty.

The ideal autonomous part is the self-adjoint $H_{1}$ on its stated domain. A required full physical propagator must separately exist and restrict to the specified sector dynamics.

A directly checkable class is

E_{1} (t) = (D_{M} (t) B (t) B (t)^{†} D_{F} (t)) on C^{d} \oplus h,

with bounded Hermitian diagonal blocks and bounded $B : C^{d} \to h$ . It includes source detuning, bounded dispersion changes, label mixing, and regular coupling changes, and obeys

∥ E_{1} (t) ∥ \leq ∥ D_{M} (t) ∥ + ∥ B (t) ∥ + ∥ D_{F} (t) ∥ .

Displayed formulas in this passage

Hawk02-C@2#eq:Eblock · line 1354
$E_{1} (t) = (D_{M} (t) B (t) B (t)^{†} D_{F} (t)) on C^{d} \oplus h,$
unlabeled · line 1345
$\int_{0}^{T} ∥ E_{1} (t) ∥_{\infty} d t < \infty.$
unlabeled · line 1367
$∥ E_{1} (t) ∥ \leq ∥ D_{M} (t) ∥ + ∥ B (t) ∥ + ∥ D_{F} (t) ∥ .$

Perturbations on the checked invariant sector

Displayed formulas in this passage

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