Manuscript Em03-D@1 · Em03-D-v1.tex · section · 450d878a

Conversion to the Unruh moment topology

A quantitative transfer estimate from advanced evolution › Conversion to the Unruh moment topology · lines 1276–1295

Em03-D@1#eq:transferconstant

Abbreviate the two scalar coefficients in (eq:compactcovariancebound) by

A_{0} = \frac{1}{2} + \frac{2}{β ω _{c}}, A_{1} = \frac{1}{2 ω _{c} ^{2}} + \frac{2}{3 β ω _{c} ^{3}} .

Choose a rectangular coupling support bound $I \times [- X, X]$ , and let $V_{K} = 2 X Δ$ . Put

a_{0} = ∥ a ∥_{\infty}, a_{t} = ∥ \partial_{t} a ∥_{\infty},

L_{R} = \frac{2 V _{K} C _{X}}{2 π} A_{0} a_{0}^{2} + A_{1} (a_{t} + a_{0})^{2} .

Displayed formulas in this passage

Em03-D@1#eq:transferconstant · line 1290
$L_{R} = \frac{2 V _{K} C _{X}}{2 π} A_{0} a_{0}^{2} + A_{1} (a_{t} + a_{0})^{2} .$
unlabeled · line 1280
$A_{0} = \frac{1}{2} + \frac{2}{β ω _{c}}, A_{1} = \frac{1}{2 ω _{c} ^{2}} + \frac{2}{3 β ω _{c} ^{3}} .$
unlabeled · line 1287
$a_{0} = ∥ a ∥_{\infty}, a_{t} = ∥ \partial_{t} a ∥_{\infty},$