TFPT scientific source excerpt
Original repository path: documents/archive--tfpt-45--source_extracts--03_em_flavor_source/sections/001-section-kernel-numerics-and-electromagnetic-closure.tex
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000094 | \begin{definition}[Minimal primitive seam transfer]
000095 | \label{def:exact-seam-generating-function}
000096 | Let $\psi_{\Sigma}$ be the normalized primitive seam mode singled out by
000097 | \TFPTxref{thm:primitive-seam-generator}. Define the minimal seam transfer operator by the rank-one
000098 | projector
000099 | \[
000100 | U_{\Sigma}^{\min}:=|\psi_{\Sigma}\rangle\langle\psi_{\Sigma}|.
000101 | \]
000102 | With
000103 | \[
000104 | q(\alpha):=\deltatop e^{-2\alpha},
000105 | \qquad
000106 | B\gamma=\frac54,
000107 | \]
000108 | one has
000109 | \[
000110 | \mathcal W_{\Sigma}(\alpha)
000111 | :=
000112 | -B\gamma\,\tr_{\mathrm{adm}}\log\!\bigl(1-q(\alpha)U_{\Sigma}^{\min}\bigr)
000113 | =-\frac54\log(1-q(\alpha)).
000114 | \]
000115 | \[
000116 | \mathcal T_{\Sigma}(\alpha)=e^{\mathcal W_{\Sigma}(\alpha)}=(1-q(\alpha))^{-5/4}.
000117 | \]
000118 | \begin{equation}
000119 | \label{eq:phi-opening}
000120 | \phiseam(\alpha)=\phibase+q(\alpha)(1-q(\alpha))^{-5/4}.
000121 | \end{equation}
000122 | \end{definition}
000123 |