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

One frozen four-Majorana realization

An exact dynamical negative control › One frozen four-Majorana realization · lines 1442–1495

Hawk04-A@1#eq:zR

We can evaluate a member of the interacting family exactly, without a disorder average or an approximate scrambling premise.

Fix

N = 4, J_{1234} = J > 0, α = 1, ζ = 0, s^{'} = (1, 1),

one bath species, $g \neq = 0$ , and any fixed $0 < μ < Λ$ . Then

H_{S} = J (I - S_{1} S_{2}), A = \frac{S _{1} + S _{2}}{2} .

Take $c_{j} = (χ_{2 j - 1} + i χ_{2 j}) /2$ , so $S_{j} = 2 c_{j}^{†} c_{j} - I$ .

Prepare $∣ B_{s} ⟩ = ∣ 11 ⟩_{S}$ . Its filtered state (eq:filtered) is still $∣ 11 ⟩_{S}$ . Swap the entire two-mode diary carrier with the source. The carrier becomes the fixed state $∣ 11 ⟩_{D}$ , and the logical source states are $∣ 00 ⟩_{S}, ∣ 11 ⟩_{S}$ . Both have source energy zero, and their coupling eigenvalues are $- 1, + 1$ , respectively.

For

f (ω) = \frac{1}{2 ω},

define

η_{i} (t) = g a_{i} \frac{e ^{- i ω t} - 1}{ω} f (ω), a_{0} = - 1, a_{1} = 1.

These are square-integrable coherent amplitudes. For the declared packet projection $P_{r}$ , put

η_{i, R} (t) = P_{r} η_{i} (t), c_{R} (t) = exp [- \frac{1}{2} ∥ η_{0, R} (t) - η_{1, R} (t) ∥^{2}],

and

z_{R} (t) = 1 - c_{R} (t)^{2} .

Displayed formulas in this passage

Hawk04-A@1#eq:zR · line 1491
$z_{R} (t) = 1 - c_{R} (t)^{2} .$
unlabeled · line 1448
$N = 4, J_{1234} = J > 0, α = 1, ζ = 0, s^{'} = (1, 1),$
unlabeled · line 1454
$H_{S} = J (I - S_{1} S_{2}), A = \frac{S _{1} + S _{2}}{2} .$
unlabeled · line 1471
$f (ω) = \frac{1}{2 ω},$
unlabeled · line 1475
$η_{i} (t) = g a_{i} \frac{e ^{- i ω t} - 1}{ω} f (ω), a_{0} = - 1, a_{1} = 1.$
unlabeled · line 1484
$η_{i, R} (t) = P_{r} η_{i} (t), c_{R} (t) = exp [- \frac{1}{2} ∥ η_{0, R} (t) - η_{1, R} (t) ∥^{2}],$

One frozen four-Majorana realization

Displayed formulas in this passage

Nearby in this section