Orbit figure draft

Former-commit-id: 280b4d22178c05abe96fad4e455ca7136f2b7361
This commit is contained in:
Marek Nečada 2019-08-02 10:01:22 +03:00
parent f65efdfe73
commit 8baf3a259c
3 changed files with 40 additions and 20 deletions

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@ -7,6 +7,7 @@
\textclass article
\begin_preamble
\DeclareUnicodeCharacter{0428}{Ш }
\usepackage{tikz}
\end_preamble
\use_default_options true
\maintain_unincluded_children false

25
lepaper/orbits.tex Normal file
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@ -0,0 +1,25 @@
\tikzstyle{orbit1}=[rectangle,draw=blue!50,fill=blue!20]
\tikzstyle{orbit2}=[rectangle,draw=green!50,fill=green!20]
\begin{tikzpicture}
\draw (-4,0) -- (4,0);
\draw (0,-2) -- (0,2);
\node (O) at (0,0) [circle, draw=red!50,fill=red!20] {O};
\node (A) at (-3.0,0.5) [orbit1] {A};
\node (B) at (3.0,0.5) [orbit1] {B};
\node (C) at (3.0,-0.5) [orbit1] {C};
\node (D) at (-3.0,-0.5) [orbit1] {D};
\node (E) at (0,-1) [orbit2] {E};
\node (F) at (0,1) [orbit2] {F};
\draw [->] (A) to (B);
\draw [->] (A) to [bend right=18] (C);
\draw [->] (A) to (D);
\draw [<->] (E.east) to [bend right=30] (F.east);
\end{tikzpicture}

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@ -506,8 +506,6 @@ noprefix "false"
\end_inset
, we have
\lang english
\begin_inset Formula
\begin{multline}
\vect E\left(\omega,R_{g}\vect r\right)=\sum_{\tau=1,2}\sum_{l=1}^{\infty}\sum_{m=-l}^{+l}\sum_{m'=-l}^{l}\left(\rcoeffptlm p{\tau}lmD_{m',\mu'}^{\tau l}\left(g\right)\vswfrtlm{\tau}l{m'}\left(k\left(\vect r-R_{g}\vect r_{p}\right)\right)\right.+\\
@ -527,6 +525,18 @@ wide false
sideways false
status open
\begin_layout Plain Layout
\align center
\begin_inset CommandInset include
LatexCommand input
filename "orbits.tex"
literal "true"
\end_inset
\end_layout
\begin_layout Plain Layout
\begin_inset Caption Standard
@ -551,12 +561,12 @@ Scatterer orbits under
\end_inset
lie on the
\begin_inset Formula $xz$
\begin_inset Formula $yz$
\end_inset
plane, hence the corresponding reflection maps each of them to itself,
but the
\begin_inset Formula $yz$
\begin_inset Formula $xz$
\end_inset
reflection (or the
@ -685,8 +695,6 @@ status open
\end_inset
one has
\lang english
\begin_inset Formula
\begin{align}
\vect E\left(\omega,R_{g}\vect r\right) & =\sum_{\tau=1,2}\sum_{l=1}^{\infty}\sum_{m=-l}^{+l}\sum_{m'=-l}^{l}\left(\rcoeffptlm p{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfrtlm{\tau}l{m'}\left(k\left(\vect r-\vect r_{\pi_{g}(p)}\right)\right)\right.+\label{eq:rotated E field expansion around outside origin-1}\\
@ -726,8 +734,6 @@ noprefix "false"
\end_layout
\begin_layout Standard
\lang english
\begin_inset Formula
\begin{align}
\rcoeff & \mapsto J\left(g\right)a,\nonumber \\
@ -741,8 +747,6 @@ noprefix "false"
status open
\begin_layout Plain Layout
\lang english
The matrices
\begin_inset Formula $D\left(g\right)$
\end_inset
@ -1184,8 +1188,6 @@ name "Phase factor illustration"
\begin_layout Standard
More rigorous analysis can be found e.g.
in
\lang english
\begin_inset CommandInset citation
LatexCommand cite
after "chapters 1011"
@ -1211,14 +1213,10 @@ In the group-theoretical terminology, blablabla little groups blabla bla...
\end_layout
\begin_layout Standard
\lang english
\begin_inset Note Note
status open
\begin_layout Plain Layout
\lang english
A general overview of utilizing group theory to find lattice modes at high-symme
try points of the Brillouin zone can be found e.g.
in
@ -1234,8 +1232,6 @@ literal "true"
\end_layout
\begin_layout Plain Layout
\lang english
We analyse the symmetries of the system in the same VSWF representation
as used in the
\begin_inset Formula $T$
@ -1389,8 +1385,6 @@ where
\end_layout
\begin_layout Plain Layout
\lang english
Each mode at the
\begin_inset Formula $\Kp$
\end_inset