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More Päivi's suggestions implemented. 

Former-commit-id: f391fdb73b126a241e3900d5282841f03abd5fb0
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Marek Nečada 2020-06-16 21:47:30 +03:00
parent 8942753a13
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3 changed files with 85 additions and 32 deletions
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25
lepaper/Tmatrix.bib
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@ -76,6 +76,14 @@
series = {Artech {{House Antennas}} and {{Propagation Library}}} series = {Artech {{House Antennas}} and {{Propagation Library}}}
} }
@book{condon_theory_1935,
title = {The {{Theory}} of {{Atomic Spectra}}},
author = {Condon, E. U. and Shortley, G. H.},
year = {1935},
publisher = {{Cambridge University Press}},
isbn = {978-0-521-09209-8}
}
@article{dellnitz_locating_2002, @article{dellnitz_locating_2002,
title = {Locating All the Zeros of an Analytic Function in One Complex Variable}, title = {Locating All the Zeros of an Analytic Function in One Complex Variable},
author = {Dellnitz, Michael and Sch{\"u}tze, Oliver and Zheng, Qinghua}, author = {Dellnitz, Michael and Sch{\"u}tze, Oliver and Zheng, Qinghua},
@ -945,6 +953,13 @@ matrix method for multilayer calculations.},
number = {4} number = {4}
} }
@misc{SCUFF/MMN,
title = {{{SCUFF}}-{{EM}}},
author = {Reid, Homer},
year = {2018},
note = {https://github.com/texnokrates/scuff-em}
}
@misc{SCUFF2, @misc{SCUFF2,
title = {{{SCUFF}}-{{EM}}}, title = {{{SCUFF}}-{{EM}}},
author = {Reid, Homer}, author = {Reid, Homer},
@ -1147,6 +1162,16 @@ matrix method for multilayer calculations.},
number = {8} number = {8}
} }
@book{wigner_group_1959,
title = {Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra},
author = {Wigner, Eugene P. and Griffin, J. J.},
year = {1959},
edition = {Revised},
publisher = {{Academic Press}},
file = {/home/mmn/.zotero/zotero/w4aj0ekp.default/zotero/storage/8T5VQVHL/Group theory and its application to the quantum mechanics of atomic spectra by Eugene P. Wigner, J. J. Griffin (z-lib.org).djvu},
isbn = {978-0-12-750550-3}
}
@article{xu_calculation_1996, @article{xu_calculation_1996,
title = {Calculation of the {{Addition Coefficients}} in {{Electromagnetic Multisphere}}-{{Scattering Theory}}}, title = {Calculation of the {{Addition Coefficients}} in {{Electromagnetic Multisphere}}-{{Scattering Theory}}},
author = {Xu, Yu-lin}, author = {Xu, Yu-lin},

6
lepaper/infinite.lyx
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@ -2205,9 +2205,9 @@ noprefix "false"
, taking the sums over scatterers inside one unit cell, to get the extinction , taking the sums over scatterers inside one unit cell, to get the extinction
and absorption cross sections per unit cell. and absorption cross sections per unit cell.
From these, quantities such as absorption, extinction coefficients are From these, quantities such as absorption, extinction and scattering coefficien
obtained using suitable normalisation by unit cell size, depending on lattice ts are obtained using suitable normalisation by unit cell size, depending
dimensionality. on lattice dimensionality.
\end_layout \end_layout
\begin_layout Standard \begin_layout Standard

86
lepaper/symmetries.lyx
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@ -207,11 +207,11 @@ TODO Zkontrolovat všechny vzorečky zde!!!
In order to make use of the point group symmetries, we first need to know In order to make use of the point group symmetries, we first need to know
how they affect our basis functions, i.e. how they affect our basis functions, i.e.
the VSWFs. \begin_inset space \space{}
\end_layout \end_inset
\begin_layout Standard the VSWFs.
Let Let
\begin_inset Formula $g$ \begin_inset Formula $g$
\end_inset \end_inset
@ -220,8 +220,10 @@ Let
\end_inset \end_inset
, i.e. , i.e.
a 3D point rotation or reflection operation that transforms vectors in \begin_inset space \space{}
\end_inset
a 3D point rotation or reflection operation that transforms vectors in
\begin_inset Formula $\reals^{3}$ \begin_inset Formula $\reals^{3}$
\end_inset \end_inset
@ -281,8 +283,8 @@ Spherical harmonics
, transform as , transform as
\begin_inset CommandInset citation \begin_inset CommandInset citation
LatexCommand cite LatexCommand cite
after "???" after "Chapter 15"
key "dresselhaus_group_2008" key "wigner_group_1959"
literal "false" literal "false"
\end_inset \end_inset
@ -429,11 +431,11 @@ noprefix "false"
\end_inset \end_inset
(and analogously for the regular waves and analogously for the regular waves
\begin_inset Formula $\vswfrtlm{\tau}lm$ \begin_inset Formula $\vswfrtlm{\tau}lm$
\end_inset \end_inset
). .
\begin_inset Note Note \begin_inset Note Note
status open status open
@ -767,7 +769,7 @@ With these transformation properties in hand, we can proceed to the effects
& =\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(\kappa\left(\vect r-\vect r_{\pi_{g}p}\right)\right)\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(\kappa\left(\vect r-\vect r_{\pi_{g}p}\right)\right)\right.\\
& \quad+\left.\outcoeffptlm p{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfouttlm{\tau}l{m'}\left(\kappa\left(\vect r-\vect r_{\pi_{g}p}\right)\right)\right)\\ & \quad+\left.\outcoeffptlm p{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfouttlm{\tau}l{m'}\left(\kappa\left(\vect r-\vect r_{\pi_{g}p}\right)\right)\right)\\
& =\sum_{\tau=1,2}\sum_{l=1}^{\infty}\sum_{m=-l}^{+l}\sum_{m'=-l}^{l}\left(\rcoeffptlm{\pi_{g}^{-1}q}{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfrtlm{\tau}l{m'}\left(\kappa\left(\vect r-\vect r_{q}\right)\right)\right.\\ & =\sum_{\tau=1,2}\sum_{l=1}^{\infty}\sum_{m=-l}^{+l}\sum_{m'=-l}^{l}\left(\rcoeffptlm{\pi_{g}^{-1}q}{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfrtlm{\tau}l{m'}\left(\kappa\left(\vect r-\vect r_{q}\right)\right)\right.\\
& \quad+\left.\outcoeffptlm{\pi_{g}^{-1}q}{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfouttlm{\tau}l{m'}\left(\kappa\left(\vect r-\vect r_{q}\right)\right)\right) & \quad+\left.\outcoeffptlm{\pi_{g}^{-1}q}{\tau}lmD_{m,\mu'}^{\tau l}\left(g\right)\vswfouttlm{\tau}l{m'}\left(\kappa\left(\vect r-\vect r_{q}\right)\right)\right).
\end{align*} \end{align*}
\end_inset \end_inset
@ -799,7 +801,11 @@ For a given particle
\begin_inset Formula $p$ \begin_inset Formula $p$
\end_inset \end_inset
, i.e. ,
\begin_inset space \space{}
\end_inset
i.e.
the set the set
\begin_inset Formula $\left\{ \pi_{g}\left(p\right);g\in G\right\} $ \begin_inset Formula $\left\{ \pi_{g}\left(p\right);g\in G\right\} $
\end_inset \end_inset
@ -853,7 +859,17 @@ noprefix "false"
\end_inset \end_inset
(TODO avoid notation clash here in a more consistent and readable way!)
\begin_inset Note Note
status open
\begin_layout Plain Layout
(TODO avoid notation clash here in a more consistent and readable way!)
\end_layout
\end_inset
\begin_inset Formula \begin_inset Formula
\begin{align} \begin{align}
\rcoeffp p & \overset{g}{\longmapsto}\tilde{J}\left(g\right)\rcoeffp{\pi_{g}^{-1}(p)},\nonumber \\ \rcoeffp p & \overset{g}{\longmapsto}\tilde{J}\left(g\right)\rcoeffp{\pi_{g}^{-1}(p)},\nonumber \\
@ -942,7 +958,7 @@ ing problem matrix
\begin_inset Formula $G$ \begin_inset Formula $G$
\end_inset \end_inset
consisting of matrices consisting of matrices
\begin_inset Formula $D^{\Gamma_{n}}\left(g\right)$ \begin_inset Formula $D^{\Gamma_{n}}\left(g\right)$
\end_inset \end_inset
@ -1050,7 +1066,7 @@ literal "false"
or or
\begin_inset CommandInset citation \begin_inset CommandInset citation
LatexCommand cite LatexCommand cite
after "???" after "Chapter 2"
key "bradley_mathematical_1972" key "bradley_mathematical_1972"
literal "false" literal "false"
@ -1187,7 +1203,10 @@ Also for periodic systems,
\end_inset \end_inset
from the left hand side of eqs. from the left hand side of eqs.
\begin_inset space \space{}
\end_inset
\begin_inset CommandInset ref \begin_inset CommandInset ref
LatexCommand eqref LatexCommand eqref
reference "eq:Multiple-scattering problem unit cell block form" reference "eq:Multiple-scattering problem unit cell block form"
@ -1230,7 +1249,7 @@ s happens unless
lies somewhere in the high-symmetry parts of the Brillouin zone. lies somewhere in the high-symmetry parts of the Brillouin zone.
However, the high-symmetry points are usually the ones of the highest physical However, the high-symmetry points are usually the ones of the highest physical
interest, for it is where the band edges are typically located. interest, for it is where the band edges are typically located.
The subsection does not aim for an exhaustive treatment of the topic of This subsection does not aim for an exhaustive treatment of the topic of
space groups in physics (which can be found elsewhere space groups in physics (which can be found elsewhere
\begin_inset CommandInset citation \begin_inset CommandInset citation
LatexCommand cite LatexCommand cite
@ -1414,7 +1433,10 @@ The transformation to the symmetry adapted basis
: this can happen if the point group symmetry maps some of the scatterers : this can happen if the point group symmetry maps some of the scatterers
from the reference unit cell to scatterers belonging to other unit cells. from the reference unit cell to scatterers belonging to other unit cells.
This is illustrated in Fig. This is illustrated in Fig.
\begin_inset space \space{}
\end_inset
\begin_inset CommandInset ref \begin_inset CommandInset ref
LatexCommand ref LatexCommand ref
reference "Phase factor illustration" reference "Phase factor illustration"
@ -1426,7 +1448,10 @@ noprefix "false"
. .
Fig. Fig.
\begin_inset space \space{}
\end_inset
\begin_inset CommandInset ref \begin_inset CommandInset ref
LatexCommand ref LatexCommand ref
reference "Phase factor illustration" reference "Phase factor illustration"
@ -1449,21 +1474,21 @@ a shows a hexagonal periodic array with
\end_inset \end_inset
. .
If we delimit our representative unit cell as the Wigner-Seitz cell with We delimit our representative unit cell as the Wigner-Seitz cell with origin
origin in a in a
\begin_inset Formula $D_{6}$ \begin_inset Formula $D_{6}$
\end_inset \end_inset
point group symmetry center (there is one per each unit cell). point group symmetry center (there is one per each unit cell); per unit
Per unit cell, there are five different particles placed on the unit cell cell, there are five different particles placed on the unit cell boundary,
boundary, and we need to make a choice to which unit cell the particles and we need to make a choice to which unit cell the particles on the boundary
on the boundary belong; in our case, we choose that a unit cell includes belong; in our case, we choose that a unit cell includes the particles
the particles on the left as denoted by different colors. on the left as denoted by different colors.
If the Bloch vector is at the upper If the Bloch vector is at the upper
\begin_inset Formula $M$ \begin_inset Formula $M$
\end_inset \end_inset
point, point,
\begin_inset Formula $\vect k=\vect M_{1}=\left(0,2\pi/\sqrt{3}a\right)$ \begin_inset Formula $\vect k=\vect M_{1}=\left(0,2\pi/\sqrt{3}a\right)$
\end_inset \end_inset
@ -1503,7 +1528,10 @@ horizontal
\end_inset \end_inset
as in eq. as in eq.
\begin_inset space \space{}
\end_inset
\begin_inset CommandInset ref \begin_inset CommandInset ref
LatexCommand eqref LatexCommand eqref
reference "eq:excitation coefficient under symmetry operation" reference "eq:excitation coefficient under symmetry operation"
@ -1577,7 +1605,7 @@ If we set instead
\begin_inset Formula $\vect k=\vect K=\left(4\pi/3a,0\right),$ \begin_inset Formula $\vect k=\vect K=\left(4\pi/3a,0\right),$
\end_inset \end_inset
the original the original
\begin_inset Formula $D_{6}$ \begin_inset Formula $D_{6}$
\end_inset \end_inset