Manuscript Hawk02-D@1 · Hawk02-D.tex · section · e6e4b72f

Energy transfer from the same dynamics

Energy transfer from the same dynamics · lines 1063–1091

Split the Hamiltonian into

H = H_{S} + H_{B} + H_{int},

where

H_{S} H_{B} H_{int} = ω_{0} a \sum f_{0, a}^{†} f_{0, a}, = ω_{0} a \sum j \geq 1 \sum f_{j, a}^{†} f_{j, a} + c a \sum j \geq 1 \sum (f_{j, a}^{†} f_{j + 1, a} + f_{j + 1, a}^{†} f_{j, a}), = c a \sum (f_{0, a}^{†} f_{1, a} + f_{1, a}^{†} f_{0, a}) .

These are well defined on every bounded-particle sector used by the preparation.

For an input $ρ$ , let

k ˉ (ρ) = Tr (N_{S} W ρ W^{†}) .

Displayed formulas in this passage

unlabeled · line 1070
$H_{S} H_{B} H_{int} = ω_{0} a \sum f_{0, a}^{†} f_{0, a}, = ω_{0} a \sum j \geq 1 \sum f_{j, a}^{†} f_{j, a} + c a \sum j \geq 1 \sum (f_{j, a}^{†} f_{j + 1, a} + f_{j + 1, a}^{†} f_{j, a}), = c a \sum (f_{0, a}^{†} f_{1, a} + f_{1, a}^{†} f_{0, a}) .$
unlabeled · line 1066
$H = H_{S} + H_{B} + H_{int},$
unlabeled · line 1088
$k ˉ (ρ) = Tr (N_{S} W ρ W^{†}) .$