Manuscript Em03-H@8 · Em03-H-v8.tex · section · 91e9e3bd

Bath and signed access

Frozen microscopic model and complete preparation › Bath and signed access · lines 426–451

Em03-H@8#eq:regroup

Use an independent initially vacuum bath $H_{R} = F_{f} (C^{n})$ , with

H_{R} = Ω N_{R}, N_{R} = j \sum b_{j}^{†} b_{j}, N_{tot} = N_{B} + N_{R}, Ω > 0,

G_{hop} = j \sum (c_{j}^{†} b_{j} + b_{j}^{†} c_{j}) .

The one-particle order is $c_{1}, \dots, c_{n}, b_{1}, \dots, b_{n}$ . Odd operators in the two blocks anticommute. Pair hopping terms commute and $∥ G_{hop} ∥ \leq n$ .

The signed regrouping $R_{A}$ places accessible modes first, preserving each declared internal order. For whole-bath access,

R_{R} (∣ L ⟩_{B} ∣ T ⟩_{R}) = (- 1)^{∣ L ∣∣ T ∣} ∣ T ⟩_{R} ∣ L ⟩_{B} .

Displayed formulas in this passage

Em03-H@8#eq:regroup · line 446
$R_{R} (∣ L ⟩_{B} ∣ T ⟩_{R}) = (- 1)^{∣ L ∣∣ T ∣} ∣ T ⟩_{R} ∣ L ⟩_{B} .$
unlabeled · line 430
$H_{R} = Ω N_{R}, N_{R} = j \sum b_{j}^{†} b_{j}, N_{tot} = N_{B} + N_{R}, Ω > 0,$
unlabeled · line 435
$G_{hop} = j \sum (c_{j}^{†} b_{j} + b_{j}^{†} c_{j}) .$

Bath and signed access

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