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Fix M = WT -> M = TW + some forgotten changes. 

Former-commit-id: 4166fb78baf097b52a559ece093454450ed19fbd
This commit is contained in:
Marek Nečada 2019-08-04 18:24:17 +03:00
parent 44b8146fe2
commit 3fe357fb8a
4 changed files with 32 additions and 9 deletions
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4
lepaper/arrayscat.lyx
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@ -285,7 +285,7 @@ status open
\begin_inset FormulaMacro \begin_inset FormulaMacro
\newcommand{\rcoeffincp}[1]{a_{#1}^{\mathrm{inc.}}} \newcommand{\rcoeffincp}[1]{\tilde{a}_{#1}}
\end_inset \end_inset
@ -295,7 +295,7 @@ status open
\begin_inset FormulaMacro \begin_inset FormulaMacro
\newcommand{\rcoeffinc}{a^{\mathrm{inc.}}} \newcommand{\rcoeffinc}{\tilde{a}}
\end_inset \end_inset

9
lepaper/examples.lyx
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@ -1,5 +1,5 @@
#LyX 2.4 created this file. For more info see https://www.lyx.org/ #LyX 2.4 created this file. For more info see https://www.lyx.org/
\lyxformat 583 \lyxformat 584
\begin_document \begin_document
\begin_header \begin_header
\save_transient_properties true \save_transient_properties true
@ -95,6 +95,13 @@
\begin_layout Section \begin_layout Section
Applications Applications
\begin_inset CommandInset label
LatexCommand label
name "sec:Applications"
\end_inset
\end_layout \end_layout
\end_body \end_body

26
lepaper/infinite.lyx
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@ -1,5 +1,5 @@
#LyX 2.4 created this file. For more info see https://www.lyx.org/ #LyX 2.4 created this file. For more info see https://www.lyx.org/
\lyxformat 583 \lyxformat 584
\begin_document \begin_document
\begin_header \begin_header
\save_transient_properties true \save_transient_properties true
@ -95,6 +95,13 @@
\begin_layout Section \begin_layout Section
Infinite periodic systems Infinite periodic systems
\begin_inset CommandInset label
LatexCommand label
name "sec:Infinite"
\end_inset
\begin_inset FormulaMacro \begin_inset FormulaMacro
\newcommand{\dlv}{\vect a} \newcommand{\dlv}{\vect a}
\end_inset \end_inset
@ -325,7 +332,7 @@ As in the case of a finite system, eq.
can be written in a shorter block-matrix form, can be written in a shorter block-matrix form,
\begin_inset Formula \begin_inset Formula
\begin{equation} \begin{equation}
\left(I-WT\right)\outcoeffp{\vect 0}\left(\vect k\right)=\rcoeffincp{\vect 0}\left(\vect k\right)\label{eq:Multiple-scattering problem unit cell block form} \left(I-TW\right)\outcoeffp{\vect 0}\left(\vect k\right)=T\rcoeffincp{\vect 0}\left(\vect k\right)\label{eq:Multiple-scattering problem unit cell block form}
\end{equation} \end{equation}
\end_inset \end_inset
@ -348,7 +355,7 @@ noprefix "false"
the external driving) set to zero, the external driving) set to zero,
\begin_inset Formula \begin_inset Formula
\begin{equation} \begin{equation}
\left(I-WT\right)\outcoeffp{\vect 0}\left(\vect k\right)=0,\label{eq:lattice mode equation} \left(I-TW\right)\outcoeffp{\vect 0}\left(\vect k\right)=0,\label{eq:lattice mode equation}
\end{equation} \end{equation}
\end_inset \end_inset
@ -369,7 +376,7 @@ noprefix "false"
\end_inset \end_inset
exist if the matrix on the left-hand side exist if the matrix on the left-hand side
\begin_inset Formula $M\left(\omega,\vect k\right)=\left(I-W\left(\omega,\vect k\right)T\left(\omega\right)\right)$ \begin_inset Formula $M\left(\omega,\vect k\right)=\left(I-T\left(\omega\right)W\left(\omega,\vect k\right)\right)$
\end_inset \end_inset
is singular – this condition gives the is singular – this condition gives the
@ -710,13 +717,22 @@ where changed the sign of
. .
Fourier transform of product is convolution of Fourier transforms, so (using Fourier transform of product is convolution of Fourier transforms, so (using
formula formula
\begin_inset Note Note
status open
\begin_layout Plain Layout
\begin_inset CommandInset ref \begin_inset CommandInset ref
LatexCommand eqref LatexCommand eqref
reference "eq:Dirac comb uaFt" reference "eq:Dirac comb uaFt"
\end_inset \end_inset
for the Fourier transform of Dirac comb)
\end_layout
\end_inset
(REF?) for the Fourier transform of Dirac comb)
\begin_inset Formula \begin_inset Formula
\begin{eqnarray} \begin{eqnarray}
W_{\alpha\beta}(\vect k) & = & \left(\left(\uaft{\dc{\basis u}}\right)\ast\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\right)(\vect k)\nonumber \\ W_{\alpha\beta}(\vect k) & = & \left(\left(\uaft{\dc{\basis u}}\right)\ast\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\right)(\vect k)\nonumber \\

2
lepaper/symmetries.lyx
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@ -1061,7 +1061,7 @@ Periodic systems
\begin_layout Standard \begin_layout Standard
For periodic systems, we can in similar manner also block-diagonalise the For periodic systems, we can in similar manner also block-diagonalise the
\begin_inset Formula $M\left(\omega,\vect k\right)=\left(I-W\left(\omega,\vect k\right)T\left(\omega\right)\right)$ \begin_inset Formula $M\left(\omega,\vect k\right)=\left(I-T\left(\omega\right)W\left(\omega,\vect k\right)\right)$
\end_inset \end_inset
from the left hand side of eqs. from the left hand side of eqs.