Futile attempts to make the lyx document compile
Former-commit-id: d164c56e3eedb01db150844cc6eb33aabc065d0d
This commit is contained in:
Marek Nečada
parent
0f1ce6122e
commit
f99fd5abe3
|
|
@ -5,18 +5,21 @@
|
|||
\save_transient_properties true
|
||||
\origin unavailable
|
||||
\textclass article
|
||||
\begin_preamble
|
||||
\DeclareUnicodeCharacter{0428}{Ш }
|
||||
\end_preamble
|
||||
\use_default_options true
|
||||
\maintain_unincluded_children false
|
||||
\language english
|
||||
\language_package default
|
||||
\inputencoding auto-legacy
|
||||
\inputencoding utf8
|
||||
\fontencoding auto
|
||||
\font_roman "default" "TeX Gyre Pagella"
|
||||
\font_sans "default" "default"
|
||||
\font_typewriter "default" "default"
|
||||
\font_math "auto" "auto"
|
||||
\font_default_family default
|
||||
\use_non_tex_fonts true
|
||||
\use_non_tex_fonts false
|
||||
\font_sc false
|
||||
\font_roman_osf true
|
||||
\font_sans_osf false
|
||||
|
|
@ -26,10 +29,12 @@
|
|||
\use_microtype false
|
||||
\use_dash_ligatures true
|
||||
\graphics default
|
||||
\default_output_format pdf4
|
||||
\default_output_format default
|
||||
\output_sync 0
|
||||
\bibtex_command default
|
||||
\index_command default
|
||||
\float_placement class
|
||||
\float_alignment class
|
||||
\paperfontsize default
|
||||
\spacing single
|
||||
\use_hyperref true
|
||||
|
|
@ -270,12 +275,12 @@
|
|||
|
||||
|
||||
\begin_inset FormulaMacro
|
||||
\newcommand{\rcoeffptlm}[4]{\rcoeffp{#1}_{#2#3#4}}
|
||||
\newcommand{\rcoeffptlm}[4]{\rcoeffp{#1,#2#3#4}}
|
||||
\end_inset
|
||||
|
||||
|
||||
\begin_inset FormulaMacro
|
||||
\newcommand{\rcoeffincptlm}[4]{\rcoeffincp{#1}_{#2#3#4}}
|
||||
\newcommand{\rcoeffincptlm}[4]{\rcoeffincp{#1,#2#3#4}}
|
||||
\end_inset
|
||||
|
||||
|
||||
|
|
@ -290,7 +295,7 @@
|
|||
|
||||
|
||||
\begin_inset FormulaMacro
|
||||
\newcommand{\outcoeffptlm}[4]{\outcoeffp{#1}_{#2#3#4}}
|
||||
\newcommand{\outcoeffptlm}[4]{\outcoeffp{#1,#2#3#4}}
|
||||
\end_inset
|
||||
|
||||
|
||||
|
|
@ -397,6 +402,11 @@ These are compatibility macros for the (...)-old files:
|
|||
\end_inset
|
||||
|
||||
|
||||
\begin_inset FormulaMacro
|
||||
\newcommand{\Kp}{K}
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Title
|
||||
|
|
@ -675,6 +685,17 @@ literal "true"
|
|||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
\begin_inset CommandInset include
|
||||
LatexCommand include
|
||||
filename "infinite-old.lyx"
|
||||
literal "true"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
|
|
|||
|
|
@ -1,29 +1,37 @@
|
|||
#LyX 2.1 created this file. For more info see http://www.lyx.org/
|
||||
\lyxformat 474
|
||||
#LyX 2.4 created this file. For more info see https://www.lyx.org/
|
||||
\lyxformat 583
|
||||
\begin_document
|
||||
\begin_header
|
||||
\save_transient_properties true
|
||||
\origin unavailable
|
||||
\textclass article
|
||||
\use_default_options true
|
||||
\maintain_unincluded_children false
|
||||
\language finnish
|
||||
\language english
|
||||
\language_package default
|
||||
\inputencoding auto
|
||||
\fontencoding global
|
||||
\font_roman TeX Gyre Pagella
|
||||
\font_sans default
|
||||
\font_typewriter default
|
||||
\font_math auto
|
||||
\inputencoding utf8
|
||||
\fontencoding auto
|
||||
\font_roman "default" "TeX Gyre Pagella"
|
||||
\font_sans "default" "default"
|
||||
\font_typewriter "default" "default"
|
||||
\font_math "auto" "auto"
|
||||
\font_default_family default
|
||||
\use_non_tex_fonts true
|
||||
\use_non_tex_fonts false
|
||||
\font_sc false
|
||||
\font_osf true
|
||||
\font_sf_scale 100
|
||||
\font_tt_scale 100
|
||||
\font_roman_osf true
|
||||
\font_sans_osf false
|
||||
\font_typewriter_osf false
|
||||
\font_sf_scale 100 100
|
||||
\font_tt_scale 100 100
|
||||
\use_microtype false
|
||||
\use_dash_ligatures true
|
||||
\graphics default
|
||||
\default_output_format pdf4
|
||||
\default_output_format default
|
||||
\output_sync 0
|
||||
\bibtex_command default
|
||||
\index_command default
|
||||
\float_placement class
|
||||
\float_alignment class
|
||||
\paperfontsize default
|
||||
\spacing single
|
||||
\use_hyperref true
|
||||
|
|
@ -59,6 +67,8 @@
|
|||
\suppress_date false
|
||||
\justification true
|
||||
\use_refstyle 1
|
||||
\use_minted 0
|
||||
\use_lineno 0
|
||||
\index Index
|
||||
\shortcut idx
|
||||
\color #008000
|
||||
|
|
@ -67,10 +77,14 @@
|
|||
\tocdepth 3
|
||||
\paragraph_separation indent
|
||||
\paragraph_indentation default
|
||||
\quotes_language swedish
|
||||
\is_math_indent 0
|
||||
\math_numbering_side default
|
||||
\quotes_style english
|
||||
\dynamic_quotes 0
|
||||
\papercolumns 1
|
||||
\papersides 1
|
||||
\paperpagestyle default
|
||||
\tablestyle default
|
||||
\tracking_changes false
|
||||
\output_changes false
|
||||
\html_math_output 0
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
#LyX 2.3 created this file. For more info see http://www.lyx.org/
|
||||
\lyxformat 544
|
||||
#LyX 2.4 created this file. For more info see https://www.lyx.org/
|
||||
\lyxformat 583
|
||||
\begin_document
|
||||
\begin_header
|
||||
\save_transient_properties true
|
||||
|
|
@ -7,27 +7,31 @@
|
|||
\textclass article
|
||||
\use_default_options true
|
||||
\maintain_unincluded_children false
|
||||
\language finnish
|
||||
\language english
|
||||
\language_package default
|
||||
\inputencoding auto
|
||||
\fontencoding global
|
||||
\inputencoding utf8
|
||||
\fontencoding auto
|
||||
\font_roman "default" "TeX Gyre Pagella"
|
||||
\font_sans "default" "default"
|
||||
\font_typewriter "default" "default"
|
||||
\font_math "auto" "auto"
|
||||
\font_default_family default
|
||||
\use_non_tex_fonts true
|
||||
\use_non_tex_fonts false
|
||||
\font_sc false
|
||||
\font_osf true
|
||||
\font_roman_osf true
|
||||
\font_sans_osf false
|
||||
\font_typewriter_osf false
|
||||
\font_sf_scale 100 100
|
||||
\font_tt_scale 100 100
|
||||
\use_microtype false
|
||||
\use_dash_ligatures true
|
||||
\graphics default
|
||||
\default_output_format pdf4
|
||||
\default_output_format default
|
||||
\output_sync 0
|
||||
\bibtex_command default
|
||||
\index_command default
|
||||
\float_placement class
|
||||
\float_alignment class
|
||||
\paperfontsize default
|
||||
\spacing single
|
||||
\use_hyperref true
|
||||
|
|
@ -63,6 +67,7 @@
|
|||
\justification true
|
||||
\use_refstyle 1
|
||||
\use_minted 0
|
||||
\use_lineno 0
|
||||
\index Index
|
||||
\shortcut idx
|
||||
\color #008000
|
||||
|
|
@ -73,11 +78,12 @@
|
|||
\paragraph_indentation default
|
||||
\is_math_indent 0
|
||||
\math_numbering_side default
|
||||
\quotes_style swedish
|
||||
\quotes_style english
|
||||
\dynamic_quotes 0
|
||||
\papercolumns 1
|
||||
\papersides 1
|
||||
\paperpagestyle default
|
||||
\tablestyle default
|
||||
\tracking_changes false
|
||||
\output_changes false
|
||||
\html_math_output 0
|
||||
|
|
|
|||
|
|
@ -7,16 +7,16 @@
|
|||
\textclass article
|
||||
\use_default_options true
|
||||
\maintain_unincluded_children false
|
||||
\language finnish
|
||||
\language english
|
||||
\language_package default
|
||||
\inputencoding auto-legacy
|
||||
\inputencoding utf8
|
||||
\fontencoding auto
|
||||
\font_roman "default" "TeX Gyre Pagella"
|
||||
\font_sans "default" "default"
|
||||
\font_typewriter "default" "default"
|
||||
\font_math "auto" "auto"
|
||||
\font_default_family default
|
||||
\use_non_tex_fonts true
|
||||
\use_non_tex_fonts false
|
||||
\font_sc false
|
||||
\font_roman_osf true
|
||||
\font_sans_osf false
|
||||
|
|
@ -26,10 +26,12 @@
|
|||
\use_microtype false
|
||||
\use_dash_ligatures false
|
||||
\graphics default
|
||||
\default_output_format pdf4
|
||||
\default_output_format default
|
||||
\output_sync 0
|
||||
\bibtex_command default
|
||||
\index_command default
|
||||
\float_placement class
|
||||
\float_alignment class
|
||||
\paperfontsize default
|
||||
\spacing single
|
||||
\use_hyperref true
|
||||
|
|
@ -77,7 +79,7 @@
|
|||
\paragraph_indentation default
|
||||
\is_math_indent 0
|
||||
\math_numbering_side default
|
||||
\quotes_style swedish
|
||||
\quotes_style english
|
||||
\dynamic_quotes 0
|
||||
\papercolumns 1
|
||||
\papersides 1
|
||||
|
|
|
|||
|
|
@ -1,29 +1,37 @@
|
|||
#LyX 2.1 created this file. For more info see http://www.lyx.org/
|
||||
\lyxformat 474
|
||||
#LyX 2.4 created this file. For more info see https://www.lyx.org/
|
||||
\lyxformat 583
|
||||
\begin_document
|
||||
\begin_header
|
||||
\save_transient_properties true
|
||||
\origin unavailable
|
||||
\textclass article
|
||||
\use_default_options true
|
||||
\maintain_unincluded_children false
|
||||
\language finnish
|
||||
\language english
|
||||
\language_package default
|
||||
\inputencoding auto
|
||||
\fontencoding global
|
||||
\font_roman TeX Gyre Pagella
|
||||
\font_sans default
|
||||
\font_typewriter default
|
||||
\font_math auto
|
||||
\inputencoding utf8
|
||||
\fontencoding auto
|
||||
\font_roman "default" "TeX Gyre Pagella"
|
||||
\font_sans "default" "default"
|
||||
\font_typewriter "default" "default"
|
||||
\font_math "auto" "auto"
|
||||
\font_default_family default
|
||||
\use_non_tex_fonts true
|
||||
\use_non_tex_fonts false
|
||||
\font_sc false
|
||||
\font_osf true
|
||||
\font_sf_scale 100
|
||||
\font_tt_scale 100
|
||||
\font_roman_osf true
|
||||
\font_sans_osf false
|
||||
\font_typewriter_osf false
|
||||
\font_sf_scale 100 100
|
||||
\font_tt_scale 100 100
|
||||
\use_microtype false
|
||||
\use_dash_ligatures false
|
||||
\graphics default
|
||||
\default_output_format pdf4
|
||||
\default_output_format default
|
||||
\output_sync 0
|
||||
\bibtex_command default
|
||||
\index_command default
|
||||
\float_placement class
|
||||
\float_alignment class
|
||||
\paperfontsize default
|
||||
\spacing single
|
||||
\use_hyperref true
|
||||
|
|
@ -59,6 +67,8 @@
|
|||
\suppress_date false
|
||||
\justification true
|
||||
\use_refstyle 1
|
||||
\use_minted 0
|
||||
\use_lineno 0
|
||||
\index Index
|
||||
\shortcut idx
|
||||
\color #008000
|
||||
|
|
@ -67,10 +77,14 @@
|
|||
\tocdepth 3
|
||||
\paragraph_separation indent
|
||||
\paragraph_indentation default
|
||||
\quotes_language swedish
|
||||
\is_math_indent 0
|
||||
\math_numbering_side default
|
||||
\quotes_style english
|
||||
\dynamic_quotes 0
|
||||
\papercolumns 1
|
||||
\papersides 1
|
||||
\paperpagestyle default
|
||||
\tablestyle default
|
||||
\tracking_changes false
|
||||
\output_changes false
|
||||
\html_math_output 0
|
||||
|
|
@ -81,12 +95,10 @@
|
|||
\begin_body
|
||||
|
||||
\begin_layout Subsection
|
||||
|
||||
\lang english
|
||||
The multiple-scattering problem
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "sub:The-multiple-scattering-problem"
|
||||
name "subsec:The-multiple-scattering-problem"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
|
@ -94,8 +106,6 @@ name "sub:The-multiple-scattering-problem"
|
|||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
In the
|
||||
\begin_inset Formula $T$
|
||||
\end_inset
|
||||
|
|
@ -147,6 +157,7 @@ where
|
|||
LatexCommand cite
|
||||
after "chapter 7"
|
||||
key "kristensson_scattering_2016"
|
||||
literal "true"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
|
@ -183,8 +194,6 @@ The expansion coefficients
|
|||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
At a given frequency, assuming the system is linear, the relation between
|
||||
the expansion coefficients in the VSWF bases is given by the so-called
|
||||
|
||||
|
|
@ -226,6 +235,7 @@ th nanoparticles) its elements drop very quickly to negligible values with
|
|||
\begin_inset CommandInset citation
|
||||
LatexCommand cite
|
||||
key "SCUFF2,reid_efficient_2015"
|
||||
literal "true"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
|
@ -233,8 +243,6 @@ key "SCUFF2,reid_efficient_2015"
|
|||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
The singular VSWFs originating at
|
||||
\begin_inset Formula $\vect R_{n}$
|
||||
\end_inset
|
||||
|
|
@ -262,6 +270,7 @@ Analytical expressions for the translation operator
|
|||
\begin_inset CommandInset citation
|
||||
LatexCommand cite
|
||||
key "xu_efficient_1998"
|
||||
literal "true"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
|
@ -269,8 +278,6 @@ key "xu_efficient_1998"
|
|||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
If we write the field incident onto the
|
||||
\begin_inset Formula $n$
|
||||
\end_inset
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
#LyX 2.3 created this file. For more info see http://www.lyx.org/
|
||||
\lyxformat 544
|
||||
#LyX 2.4 created this file. For more info see https://www.lyx.org/
|
||||
\lyxformat 583
|
||||
\begin_document
|
||||
\begin_header
|
||||
\save_transient_properties true
|
||||
|
|
@ -7,27 +7,31 @@
|
|||
\textclass article
|
||||
\use_default_options true
|
||||
\maintain_unincluded_children false
|
||||
\language finnish
|
||||
\language english
|
||||
\language_package default
|
||||
\inputencoding auto
|
||||
\fontencoding global
|
||||
\inputencoding utf8
|
||||
\fontencoding auto
|
||||
\font_roman "default" "TeX Gyre Pagella"
|
||||
\font_sans "default" "default"
|
||||
\font_typewriter "default" "default"
|
||||
\font_math "auto" "auto"
|
||||
\font_default_family default
|
||||
\use_non_tex_fonts true
|
||||
\use_non_tex_fonts false
|
||||
\font_sc false
|
||||
\font_osf true
|
||||
\font_roman_osf true
|
||||
\font_sans_osf false
|
||||
\font_typewriter_osf false
|
||||
\font_sf_scale 100 100
|
||||
\font_tt_scale 100 100
|
||||
\use_microtype false
|
||||
\use_dash_ligatures true
|
||||
\graphics default
|
||||
\default_output_format pdf4
|
||||
\default_output_format default
|
||||
\output_sync 0
|
||||
\bibtex_command default
|
||||
\index_command default
|
||||
\float_placement class
|
||||
\float_alignment class
|
||||
\paperfontsize default
|
||||
\spacing single
|
||||
\use_hyperref true
|
||||
|
|
@ -63,6 +67,7 @@
|
|||
\justification true
|
||||
\use_refstyle 1
|
||||
\use_minted 0
|
||||
\use_lineno 0
|
||||
\index Index
|
||||
\shortcut idx
|
||||
\color #008000
|
||||
|
|
@ -73,11 +78,12 @@
|
|||
\paragraph_indentation default
|
||||
\is_math_indent 0
|
||||
\math_numbering_side default
|
||||
\quotes_style swedish
|
||||
\quotes_style english
|
||||
\dynamic_quotes 0
|
||||
\papercolumns 1
|
||||
\papersides 1
|
||||
\paperpagestyle default
|
||||
\tablestyle default
|
||||
\tracking_changes false
|
||||
\output_changes false
|
||||
\html_math_output 0
|
||||
|
|
@ -92,8 +98,6 @@ Finite systems
|
|||
\end_layout
|
||||
|
||||
\begin_layout Itemize
|
||||
|
||||
\lang english
|
||||
motivation (classes of problems that this can solve: response to external
|
||||
radiation, resonances, ...)
|
||||
\begin_inset Separator latexpar
|
||||
|
|
@ -104,8 +108,6 @@ motivation (classes of problems that this can solve: response to external
|
|||
|
||||
\begin_deeper
|
||||
\begin_layout Itemize
|
||||
|
||||
\lang english
|
||||
theory
|
||||
\begin_inset Separator latexpar
|
||||
\end_inset
|
||||
|
|
@ -115,8 +117,6 @@ theory
|
|||
|
||||
\begin_deeper
|
||||
\begin_layout Itemize
|
||||
|
||||
\lang english
|
||||
T-matrix definition, basics
|
||||
\begin_inset Separator latexpar
|
||||
\end_inset
|
||||
|
|
@ -126,23 +126,17 @@ T-matrix definition, basics
|
|||
|
||||
\begin_deeper
|
||||
\begin_layout Itemize
|
||||
|
||||
\lang english
|
||||
How to get it?
|
||||
\end_layout
|
||||
|
||||
\end_deeper
|
||||
\begin_layout Itemize
|
||||
|
||||
\lang english
|
||||
translation operators (TODO think about how explicit this should be, but
|
||||
I guess it might be useful to write them to write them explicitly (but
|
||||
in the shortest possible form) in the normalisation used in my program)
|
||||
\end_layout
|
||||
|
||||
\begin_layout Itemize
|
||||
|
||||
\lang english
|
||||
employing point group symmetries and decomposing the problem to decrease
|
||||
the computational complexity (maybe separately)
|
||||
\end_layout
|
||||
|
|
@ -150,8 +144,6 @@ employing point group symmetries and decomposing the problem to decrease
|
|||
\end_deeper
|
||||
\end_deeper
|
||||
\begin_layout Subsection
|
||||
|
||||
\lang english
|
||||
Motivation
|
||||
\end_layout
|
||||
|
||||
|
|
@ -167,8 +159,6 @@ The basic idea of MSTMM is quite simple: the driving electromagnetic field
|
|||
\end_layout
|
||||
|
||||
\begin_layout Subsection
|
||||
|
||||
\lang english
|
||||
Single-particle scattering
|
||||
\end_layout
|
||||
|
||||
|
|
@ -227,8 +217,6 @@ todo define
|
|||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
Throughout this text, we will use the same normalisation conventions as
|
||||
in
|
||||
\begin_inset CommandInset citation
|
||||
|
|
@ -242,20 +230,14 @@ literal "true"
|
|||
\end_layout
|
||||
|
||||
\begin_layout Subsubsection
|
||||
|
||||
\lang english
|
||||
Spherical waves
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
\begin_inset Note Note
|
||||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
|
||||
\lang english
|
||||
TODO small note about cartesian multipoles, anapoles etc.
|
||||
(There should be some comparing paper that the Russians at META 2018 mentioned.)
|
||||
\end_layout
|
||||
|
|
@ -266,8 +248,6 @@ TODO small note about cartesian multipoles, anapoles etc.
|
|||
\end_layout
|
||||
|
||||
\begin_layout Subsubsection
|
||||
|
||||
\lang english
|
||||
T-matrix definition
|
||||
\end_layout
|
||||
|
||||
|
|
@ -276,26 +256,18 @@ Absorbed power
|
|||
\end_layout
|
||||
|
||||
\begin_layout Subsubsection
|
||||
|
||||
\lang english
|
||||
T-matrix compactness, cutoff validity
|
||||
\end_layout
|
||||
|
||||
\begin_layout Subsection
|
||||
|
||||
\lang english
|
||||
Multiple scattering
|
||||
\end_layout
|
||||
|
||||
\begin_layout Subsubsection
|
||||
|
||||
\lang english
|
||||
Translation operator
|
||||
\end_layout
|
||||
|
||||
\begin_layout Subsubsection
|
||||
|
||||
\lang english
|
||||
Numerical complexity, comparison to other methods
|
||||
\end_layout
|
||||
|
||||
|
|
|
|||
|
|
@ -1,29 +1,37 @@
|
|||
#LyX 2.1 created this file. For more info see http://www.lyx.org/
|
||||
\lyxformat 474
|
||||
#LyX 2.4 created this file. For more info see https://www.lyx.org/
|
||||
\lyxformat 583
|
||||
\begin_document
|
||||
\begin_header
|
||||
\save_transient_properties true
|
||||
\origin unavailable
|
||||
\textclass article
|
||||
\use_default_options false
|
||||
\maintain_unincluded_children false
|
||||
\language english
|
||||
\language_package none
|
||||
\inputencoding auto
|
||||
\inputencoding utf8
|
||||
\fontencoding default
|
||||
\font_roman default
|
||||
\font_sans default
|
||||
\font_typewriter default
|
||||
\font_math auto
|
||||
\font_roman "default" "default"
|
||||
\font_sans "default" "default"
|
||||
\font_typewriter "default" "default"
|
||||
\font_math "auto" "auto"
|
||||
\font_default_family default
|
||||
\use_non_tex_fonts false
|
||||
\font_sc false
|
||||
\font_osf false
|
||||
\font_sf_scale 100
|
||||
\font_tt_scale 100
|
||||
\font_roman_osf false
|
||||
\font_sans_osf false
|
||||
\font_typewriter_osf false
|
||||
\font_sf_scale 100 100
|
||||
\font_tt_scale 100 100
|
||||
\use_microtype false
|
||||
\use_dash_ligatures true
|
||||
\graphics default
|
||||
\default_output_format default
|
||||
\output_sync 0
|
||||
\bibtex_command default
|
||||
\index_command default
|
||||
\float_placement class
|
||||
\float_alignment class
|
||||
\paperfontsize default
|
||||
\spacing single
|
||||
\use_hyperref false
|
||||
|
|
@ -48,6 +56,8 @@
|
|||
\suppress_date false
|
||||
\justification true
|
||||
\use_refstyle 0
|
||||
\use_minted 0
|
||||
\use_lineno 0
|
||||
\index Index
|
||||
\shortcut idx
|
||||
\color #008000
|
||||
|
|
@ -56,10 +66,14 @@
|
|||
\tocdepth 3
|
||||
\paragraph_separation indent
|
||||
\paragraph_indentation default
|
||||
\quotes_language english
|
||||
\is_math_indent 0
|
||||
\math_numbering_side default
|
||||
\quotes_style english
|
||||
\dynamic_quotes 0
|
||||
\papercolumns 1
|
||||
\papersides 1
|
||||
\paperpagestyle default
|
||||
\tablestyle default
|
||||
\tracking_changes false
|
||||
\output_changes false
|
||||
\html_math_output 0
|
||||
|
|
@ -73,7 +87,7 @@
|
|||
Periodic systems and mode analysis
|
||||
\begin_inset CommandInset label
|
||||
LatexCommand label
|
||||
name "sub:Periodic-systems"
|
||||
name "subsec:Periodic-systems"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
|
@ -160,6 +174,7 @@ reference "eq:multiple scattering per particle a"
|
|||
\begin_inset CommandInset citation
|
||||
LatexCommand cite
|
||||
key "linton_lattice_2010"
|
||||
literal "true"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
|
@ -273,6 +288,7 @@ try points of the Brillouin zone can be found e.g.
|
|||
LatexCommand cite
|
||||
after "chapters 10–11"
|
||||
key "dresselhaus_group_2008"
|
||||
literal "true"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
|
@ -323,6 +339,7 @@ We analyse the symmetries of the system in the same VSWF representation
|
|||
LatexCommand cite
|
||||
after "eq. (11.19)"
|
||||
key "dresselhaus_group_2008"
|
||||
literal "true"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
|
@ -342,6 +359,7 @@ key "dresselhaus_group_2008"
|
|||
\begin_inset CommandInset citation
|
||||
LatexCommand cite
|
||||
key "schulz_point-group_1999"
|
||||
literal "true"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
|
@ -359,6 +377,7 @@ key "schulz_point-group_1999"
|
|||
LatexCommand cite
|
||||
after "eq. (4.28)"
|
||||
key "dresselhaus_group_2008"
|
||||
literal "true"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
|
@ -440,6 +459,7 @@ Each mode at the
|
|||
LatexCommand cite
|
||||
after "eq. (2.51)"
|
||||
key "dresselhaus_group_2008"
|
||||
literal "true"
|
||||
|
||||
\end_inset
|
||||
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
#LyX 2.3 created this file. For more info see http://www.lyx.org/
|
||||
\lyxformat 544
|
||||
#LyX 2.4 created this file. For more info see https://www.lyx.org/
|
||||
\lyxformat 583
|
||||
\begin_document
|
||||
\begin_header
|
||||
\save_transient_properties true
|
||||
|
|
@ -7,27 +7,31 @@
|
|||
\textclass article
|
||||
\use_default_options true
|
||||
\maintain_unincluded_children false
|
||||
\language finnish
|
||||
\language english
|
||||
\language_package default
|
||||
\inputencoding auto
|
||||
\fontencoding global
|
||||
\inputencoding utf8
|
||||
\fontencoding auto
|
||||
\font_roman "default" "TeX Gyre Pagella"
|
||||
\font_sans "default" "default"
|
||||
\font_typewriter "default" "default"
|
||||
\font_math "auto" "auto"
|
||||
\font_default_family default
|
||||
\use_non_tex_fonts true
|
||||
\use_non_tex_fonts false
|
||||
\font_sc false
|
||||
\font_osf true
|
||||
\font_roman_osf true
|
||||
\font_sans_osf false
|
||||
\font_typewriter_osf false
|
||||
\font_sf_scale 100 100
|
||||
\font_tt_scale 100 100
|
||||
\use_microtype false
|
||||
\use_dash_ligatures true
|
||||
\graphics default
|
||||
\default_output_format pdf4
|
||||
\default_output_format default
|
||||
\output_sync 0
|
||||
\bibtex_command default
|
||||
\index_command default
|
||||
\float_placement class
|
||||
\float_alignment class
|
||||
\paperfontsize default
|
||||
\spacing single
|
||||
\use_hyperref true
|
||||
|
|
@ -63,6 +67,7 @@
|
|||
\justification true
|
||||
\use_refstyle 1
|
||||
\use_minted 0
|
||||
\use_lineno 0
|
||||
\index Index
|
||||
\shortcut idx
|
||||
\color #008000
|
||||
|
|
@ -73,11 +78,12 @@
|
|||
\paragraph_indentation default
|
||||
\is_math_indent 0
|
||||
\math_numbering_side default
|
||||
\quotes_style swedish
|
||||
\quotes_style english
|
||||
\dynamic_quotes 0
|
||||
\papercolumns 1
|
||||
\papersides 1
|
||||
\paperpagestyle default
|
||||
\tablestyle default
|
||||
\tracking_changes false
|
||||
\output_changes false
|
||||
\html_math_output 0
|
||||
|
|
@ -92,14 +98,10 @@ Infinite periodic systems
|
|||
\end_layout
|
||||
|
||||
\begin_layout Subsection
|
||||
|
||||
\lang english
|
||||
Formulation of the problem
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
Assume a system of compact EM scatterers in otherwise homogeneous and isotropic
|
||||
medium, and assume that the system, i.e.
|
||||
both the medium and the scatterers, have linear response.
|
||||
|
|
@ -139,14 +141,10 @@ where
|
|||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
...
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
\begin_inset Formula
|
||||
\[
|
||||
\sum_{β}(\delta_{αβ}-T_{α}S_{α\leftarrowβ})A_{β}=T_{α}P_{0α}.
|
||||
|
|
@ -158,14 +156,10 @@ where
|
|||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
Now suppose that the scatterers constitute an infinite lattice
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
\begin_inset Formula
|
||||
\[
|
||||
\sum_{\vect bβ}(\delta_{\vect{ab}}\delta_{αβ}-T_{\vect aα}S_{\vect aα\leftarrow\vect bβ})A_{\vect bβ}=T_{\vect aα}P_{0\vect aα}.
|
||||
|
|
@ -225,14 +219,10 @@ W_{\alpha\beta}(\vect k)\equiv\sum_{\vect b}S_{\vect 0α\leftarrow\vect bβ}e^{i
|
|||
\end_layout
|
||||
|
||||
\begin_layout Subsection
|
||||
|
||||
\lang english
|
||||
Computing the Fourier sum of the translation operator
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
The problem evaluating
|
||||
\begin_inset CommandInset ref
|
||||
LatexCommand eqref
|
||||
|
|
@ -241,7 +231,7 @@ reference "eq:W definition"
|
|||
\end_inset
|
||||
|
||||
is the asymptotic behaviour of the translation operator,
|
||||
\begin_inset Formula $S_{\vect0α\leftarrow\vect bβ}\sim\left|\vect r_{\vect b}\right|^{-1}e^{ik_{0}\left|\vect r_{\vect b}\right|}$
|
||||
\begin_inset Formula $S_{\vect 0α\leftarrow\vect bβ}\sim\left|\vect r_{\vect b}\right|^{-1}e^{ik_{0}\left|\vect r_{\vect b}\right|}$
|
||||
\end_inset
|
||||
|
||||
that makes the convergence of the sum quite problematic for any
|
||||
|
|
@ -253,8 +243,6 @@ reference "eq:W definition"
|
|||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
|
||||
\lang english
|
||||
Note that
|
||||
\begin_inset Formula $d$
|
||||
\end_inset
|
||||
|
|
@ -274,8 +262,6 @@ Note that
|
|||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
Let us re-express the sum in
|
||||
\begin_inset CommandInset ref
|
||||
LatexCommand eqref
|
||||
|
|
@ -284,11 +270,14 @@ reference "eq:W definition"
|
|||
\end_inset
|
||||
|
||||
in terms of integral with a delta comb
|
||||
\begin_inset FormulaMacro
|
||||
\renewcommand{\basis}[1]{\mathfrak{#1}}
|
||||
\end_inset
|
||||
|
||||
|
||||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
\begin_inset Formula
|
||||
\begin{equation}
|
||||
W_{\alpha\beta}(\vect k)=\int\ud^{d}\vect r\dc{\basis u}(\vect r)S(\vect r_{\alpha}\leftarrow\vect r+\vect r_{\beta})e^{i\vect k\cdot\vect r}.\label{eq:W integral}
|
||||
|
|
@ -338,7 +327,7 @@ translation operator for spherical waves originating in
|
|||
\end_inset
|
||||
|
||||
is in fact a function of a single 3d argument,
|
||||
\begin_inset Formula $S(\vect r_{\alpha}\leftarrow\vect r+\vect r_{\beta})=S(\vect0\leftarrow\vect r+\vect r_{\beta}-\vect r_{\alpha})=S(-\vect r-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)=S(-\vect r-\vect r_{\beta}+\vect r_{\alpha})$
|
||||
\begin_inset Formula $S(\vect r_{\alpha}\leftarrow\vect r+\vect r_{\beta})=S(\vect 0\leftarrow\vect r+\vect r_{\beta}-\vect r_{\alpha})=S(-\vect r-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)=S(-\vect r-\vect r_{\beta}+\vect r_{\alpha})$
|
||||
\end_inset
|
||||
|
||||
.
|
||||
|
|
@ -352,7 +341,7 @@ reference "eq:W integral"
|
|||
can be rewritten as
|
||||
\begin_inset Formula
|
||||
\[
|
||||
W_{\alpha\beta}(\vect k)=\left(2\pi\right)^{\frac{d}{2}}\uaft{(\dc{\basis u}S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0))\left(\vect k\right)}
|
||||
W_{\alpha\beta}(\vect k)=\left(2\pi\right)^{\frac{d}{2}}\uaft{(\dc{\basis u}S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0))\left(\vect k\right)}
|
||||
\]
|
||||
|
||||
\end_inset
|
||||
|
|
@ -377,10 +366,10 @@ reference "eq:Dirac comb uaFt"
|
|||
for the Fourier transform of Dirac comb)
|
||||
\begin_inset Formula
|
||||
\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\vect0)}\right)\right)(\vect k)\nonumber \\
|
||||
& = & \frac{\left|\det\recb{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\left(\dc{\recb{\basis u}}^{(d)}\ast\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)}\right)\right)\left(\vect k\right)\nonumber \\
|
||||
& = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)}\right)\left(\vect k-\vect K\right)\label{eq:W sum in reciprocal space}\\
|
||||
& = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}e^{i\left(\vect k-\vect K\right)\cdot\left(-\vect r_{\beta}+\vect r_{\alpha}\right)}\left(\uaft{S(\vect{\bullet}\leftarrow\vect0)}\right)\left(\vect k-\vect K\right)\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 \\
|
||||
& = & \frac{\left|\det\recb{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\left(\dc{\recb{\basis u}}^{(d)}\ast\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\right)\left(\vect k\right)\nonumber \\
|
||||
& = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}\left(\uaft{S(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\left(\vect k-\vect K\right)\label{eq:W sum in reciprocal space}\\
|
||||
& = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}e^{i\left(\vect k-\vect K\right)\cdot\left(-\vect r_{\beta}+\vect r_{\alpha}\right)}\left(\uaft{S(\vect{\bullet}\leftarrow\vect 0)}\right)\left(\vect k-\vect K\right)\nonumber
|
||||
\end{eqnarray}
|
||||
|
||||
\end_inset
|
||||
|
|
@ -390,8 +379,6 @@ W_{\alpha\beta}(\vect k) & = & \left(\left(\uaft{\dc{\basis u}}\right)\ast\left(
|
|||
status open
|
||||
|
||||
\begin_layout Plain Layout
|
||||
|
||||
\lang english
|
||||
Factor
|
||||
\begin_inset Formula $\left(2\pi\right)^{\frac{d}{2}}$
|
||||
\end_inset
|
||||
|
|
@ -424,8 +411,6 @@ whole
|
|||
\end_layout
|
||||
|
||||
\begin_layout Standard
|
||||
|
||||
\lang english
|
||||
However, Fourier transform is linear, so we can in principle separate
|
||||
\begin_inset Formula $S$
|
||||
\end_inset
|
||||
|
|
@ -486,8 +471,8 @@ reference "eq:W sum in reciprocal space"
|
|||
\begin_inset Formula
|
||||
\begin{eqnarray}
|
||||
W_{\alpha\beta}\left(\vect k\right) & = & W_{\alpha\beta}^{\textup{S}}\left(\vect k\right)+W_{\alpha\beta}^{\textup{L}}\left(\vect k\right)\nonumber \\
|
||||
W_{\alpha\beta}^{\textup{S}}\left(\vect k\right) & = & \sum_{\vect R\in\basis u\ints^{d}}S^{\textup{S}}(\vect0\leftarrow\vect R+\vect r_{\beta}-\vect r_{\alpha})e^{i\vect k\cdot\vect R}\label{eq:W Short definition}\\
|
||||
W_{\alpha\beta}^{\textup{L}}\left(\vect k\right) & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}\left(\uaft{S^{\textup{L}}(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect0)}\right)\left(\vect k-\vect K\right)\label{eq:W Long definition}
|
||||
W_{\alpha\beta}^{\textup{S}}\left(\vect k\right) & = & \sum_{\vect R\in\basis u\ints^{d}}S^{\textup{S}}(\vect 0\leftarrow\vect R+\vect r_{\beta}-\vect r_{\alpha})e^{i\vect k\cdot\vect R}\label{eq:W Short definition}\\
|
||||
W_{\alpha\beta}^{\textup{L}}\left(\vect k\right) & = & \frac{\left|\det\rec{\basis u}\right|}{\left(2\pi\right)^{\frac{d}{2}}}\sum_{\vect K\in\recb{\basis u}\ints^{d}}\left(\uaft{S^{\textup{L}}(\vect{\bullet}-\vect r_{\beta}+\vect r_{\alpha}\leftarrow\vect 0)}\right)\left(\vect k-\vect K\right)\label{eq:W Long definition}
|
||||
\end{eqnarray}
|
||||
|
||||
\end_inset
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
#LyX 2.3 created this file. For more info see http://www.lyx.org/
|
||||
\lyxformat 544
|
||||
#LyX 2.4 created this file. For more info see https://www.lyx.org/
|
||||
\lyxformat 583
|
||||
\begin_document
|
||||
\begin_header
|
||||
\save_transient_properties true
|
||||
|
|
@ -7,27 +7,31 @@
|
|||
\textclass article
|
||||
\use_default_options true
|
||||
\maintain_unincluded_children false
|
||||
\language finnish
|
||||
\language english
|
||||
\language_package default
|
||||
\inputencoding auto
|
||||
\fontencoding global
|
||||
\inputencoding utf8
|
||||
\fontencoding auto
|
||||
\font_roman "default" "TeX Gyre Pagella"
|
||||
\font_sans "default" "default"
|
||||
\font_typewriter "default" "default"
|
||||
\font_math "auto" "auto"
|
||||
\font_default_family default
|
||||
\use_non_tex_fonts true
|
||||
\use_non_tex_fonts false
|
||||
\font_sc false
|
||||
\font_osf true
|
||||
\font_roman_osf true
|
||||
\font_sans_osf false
|
||||
\font_typewriter_osf false
|
||||
\font_sf_scale 100 100
|
||||
\font_tt_scale 100 100
|
||||
\use_microtype false
|
||||
\use_dash_ligatures true
|
||||
\graphics default
|
||||
\default_output_format pdf4
|
||||
\default_output_format default
|
||||
\output_sync 0
|
||||
\bibtex_command default
|
||||
\index_command default
|
||||
\float_placement class
|
||||
\float_alignment class
|
||||
\paperfontsize default
|
||||
\spacing single
|
||||
\use_hyperref true
|
||||
|
|
@ -63,6 +67,7 @@
|
|||
\justification true
|
||||
\use_refstyle 1
|
||||
\use_minted 0
|
||||
\use_lineno 0
|
||||
\index Index
|
||||
\shortcut idx
|
||||
\color #008000
|
||||
|
|
@ -73,11 +78,12 @@
|
|||
\paragraph_indentation default
|
||||
\is_math_indent 0
|
||||
\math_numbering_side default
|
||||
\quotes_style swedish
|
||||
\quotes_style english
|
||||
\dynamic_quotes 0
|
||||
\papercolumns 1
|
||||
\papersides 1
|
||||
\paperpagestyle default
|
||||
\tablestyle default
|
||||
\tracking_changes false
|
||||
\output_changes false
|
||||
\html_math_output 0
|
||||
|
|
|
|||
Loading…
Reference in New Issue