hiro/notes_io_loop
1
0
Fork 0
mirror of https://github.com/vale981/notes_io_loop synced 2025-03-05 09:31:41 -05:00
Code Issues Projects Releases Packages Wiki Activity Actions

pre-rewrite: some small typo fixes

Browse source
This commit is contained in:
Valentin Boettcher 2023-07-10 15:02:57 -04:00
parent 93a508ac69
commit 8ec258e88f
1 changed files with 2 additions and 2 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

4
roam/data/d6/e44fbc-975b-463d-87f9-878d50758b55/index.tex
View file

@ -883,7 +883,7 @@ For \(n>m\) we have
Δ_{+,-}&=2δ\\ Δ_{+,-}&=2δ\\
\label{eq:57}Δ_{n>0,-} &= n Ω_{B} + δ\\ \label{eq:57}Δ_{n>0,-} &= n Ω_{B} + δ\\
\label{eq:58}Δ_{n>0,+} &= n Ω_{B} - δ\\ \label{eq:58}Δ_{n>0,+} &= n Ω_{B} - δ\\
\label{eq:59}Δ_{n>0,m>0} &= (n-m) Ω_{B} - δ. \label{eq:59}Δ_{n>0,m>0} &= (n-m) Ω_{B}.
\end{align} \end{align}
To couple exactly one other mode with \(n>0\) to the \(+\) mode, the To couple exactly one other mode with \(n>0\) to the \(+\) mode, the
RWA requires that \(\abs{Δ_{n,+}}\neq \abs{Δ_{kl}}\) for \(k\neq n\), \(l\neq +\). RWA requires that \(\abs{Δ_{n,+}}\neq \abs{Δ_{kl}}\) for \(k\neq n\), \(l\neq +\).
@ -1009,7 +1009,7 @@ With this, we have for \(m=\pm,-N,-N+1,\ldots,-1,1,2,\ldots,N\)
\begin{equation} \begin{equation}
\label{eq:94} \label{eq:94}
\begin{aligned} \begin{aligned}
ω^{0}_{m\neq \pm} &= ω_{n}^{B} & ω^{0}_{\pm} &= \pm δ \cos(ψ)\\ ω^{0}_{m\neq \pm} &= ω_{n}^{B} & ω^{0}_{\pm} &= ω_{s} \pm δ \cos(ψ)\\
η^{0}_{m\neq\pm} &= η_{B} = η_S+2δΔ & η^{0}_{\pm} &= η_{S} + δΔ = η^{0}_{m\neq\pm} &= η_{B} = η_S+2δΔ & η^{0}_{\pm} &= η_{S} + δΔ =
\frac{η_{S}+ η_{B}}{2}. \frac{η_{S}+ η_{B}}{2}.
\end{aligned} \end{aligned}