Manuscript Psy02-A@1 · Psy02-A.tex · section · d92ce402

Displacement-compatible targets

Static concentration and normalized fluctuations › Displacement-compatible targets · lines 590–625

Psy02-A@1#eq:observable, Psy02-A@1#eq:displacement

For $0 < ϵ \leq 1$ , set

U_{ϵ} = W (d / ϵ), ρ_{ϵ} = U_{ϵ} ρ_{ϵ} U_{ϵ}^{†},

O_{j, ϵ} = b_{j} 1 + ϵ Φ (v_{j}), o_{j} = b_{j} + 2 A (d, v_{j}) .

Thus the target is displacement compatible. An arbitrary collection of numbers is not silently presumed to arise from one common displacement.

By the Weyl convention,

U_{ϵ}^{†} (O_{j, ϵ} - o_{j} 1) U_{ϵ} = ϵ Φ (v_{j}) .

Write

n_{ϵ} = Tr (ρ_{ϵ} N), C_{ϵ} = 4 n_{ϵ} + 2.

Displayed formulas in this passage

Psy02-A@1#eq:displacement · line 611
$U_{ϵ}^{†} (O_{j, ϵ} - o_{j} 1) U_{ϵ} = ϵ Φ (v_{j}) .$
unlabeled · line 593
$U_{ϵ} = W (d / ϵ), ρ_{ϵ} = U_{ϵ} ρ_{ϵ} U_{ϵ}^{†},$
Psy02-A@1#eq:observable · line 599
$O_{j, ϵ} = b_{j} 1 + ϵ Φ (v_{j}), o_{j} = b_{j} + 2 A (d, v_{j}) .$
unlabeled · line 620
$n_{ϵ} = Tr (ρ_{ϵ} N), C_{ϵ} = 4 n_{ϵ} + 2.$