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change order of indices

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Valentin Boettcher 2023-06-13 10:24:54 -04:00
parent dbc872b491
commit dae2dd1f12
1 changed files with 2 additions and 2 deletions
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roam/data/d6/e44fbc-975b-463d-87f9-878d50758b55/index.tex
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@ -519,13 +519,13 @@ find
\begin{equation}
\label{eq:39}
\ev{{b_{\outputf}(x,t)}} =
\ev{b_{\inputf}(x,t)} - ∑_{σ=\pm}∫_{0}^{τ(x,t)}χ_{σ,\sgn(x)}(τ(x,t),s) \ev{b_{\inputf,σ}(s)} \dd{s}
\ev{b_{\inputf}(x,t)} - ∑_{σ=\pm}∫_{0}^{τ(x,t)}χ_{\sgn(x),σ}(τ(x,t),s) \ev{b_{\inputf,σ}(s)} \dd{s}
\end{equation}
with the time non-local susceptibility for the left and right moving
input fields
\begin{equation}
\label{eq:40}
χ_{σ,δ}(t,s) = \frac{π n_{B}}{c}Θ(t) ∑_{γ}\pqty{U^{δ}_{γ}(t)}^\astχ_{γ}(t-s)U^{σ}_{γ}(s).
χ_{δ,σ}(t,s) = \frac{π n_{B}}{c}Θ(t) ∑_{γ}\pqty{U^{δ}_{γ}(t)}^\astχ_{γ}(t-s)U^{σ}_{γ}(s).
\end{equation}
For an input field with no left-moving components and a measurement