Manuscript Hawk04-A@1 · Hawk04-A.tex · proposition · 526092ba

Proposition: Energy in the negative control

An exact dynamical negative control › One frozen four-Majorana realization · lines 1623–1645 · proof included or linked

For the realization above,

E_{S} (t) = 0, E_{B} (t) = g^{2} \int_{μ}^{Λ} \frac{1 - cos ( ω t )}{ω ^{2}} d ω, E_{I} (t) = - E_{B} (t) .

Positive bath energy therefore coexists with no source-energy loss and with the recovery obstruction (eq:exact-negative).

Proof. The source remains in its even zero-energy eigenspace. The coherent bath energy is $h_{B}^{1/2} η_{i} (t)^{2}$ , giving the integral. The initially prepared total energy is zero, and conservation gives the interaction term.

Displayed formulas in this passage

unlabeled · line 1625
$E_{S} (t) = 0, E_{B} (t) = g^{2} \int_{μ}^{Λ} \frac{1 - cos ( ω t )}{ω ^{2}} d ω, E_{I} (t) = - E_{B} (t) .$

Nearby in this section

section: One frozen four-Majorana realization
theorem: Theorem: Exact radiation-recovery error for the frozen realization
remark: Remark: No universal positive interacting certificate follows
section: One frozen four-Majorana realization