From fd6d053dab1a2a4397a69ef35c25622b440071a1 Mon Sep 17 00:00:00 2001
From: Deepak Mallubhotla <dmallubhotla+github@gmail.com>
Date: Mon, 22 Aug 2022 19:47:19 -0500
Subject: [PATCH] feat: initial commit

---
 .gitattributes           |   1 +
 .gitignore               |  17 +++
 Makefile                 |  56 +++++++++
 README.md                |   3 +
 bibliography.bib         | 245 +++++++++++++++++++++++++++++++++++++++
 do.sh                    |  18 +++
 figures/lukemagnoise.jpg | Bin 0 -> 18303 bytes
 notes.tex                |  55 +++++++++
 8 files changed, 395 insertions(+)
 create mode 100644 .gitattributes
 create mode 100644 .gitignore
 create mode 100644 Makefile
 create mode 100644 README.md
 create mode 100644 bibliography.bib
 create mode 100644 do.sh
 create mode 100644 figures/lukemagnoise.jpg
 create mode 100644 notes.tex

diff --git a/.gitattributes b/.gitattributes
new file mode 100644
index 0000000..176a458
--- /dev/null
+++ b/.gitattributes
@@ -0,0 +1 @@
+* text=auto
diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..fca10bf
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,17 @@
+.idea
+dist
+
+*.aux
+*.fdb_latexmk
+*.fls
+*.tdo
+*.toc
+*.log
+*.pdf
+*.bbl
+*.bcf
+*.blg
+*.run.xml
+*.out
+
+*.nb
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..6dc6bee
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,56 @@
+### Build tools
+#
+LATEXMK := latexmk -pdflatex="luahblatex %O %S" -pdf -dvi- -ps- -quiet -logfilewarninglist
+WS := wolframscript -f
+
+### Directory variables
+#
+PDF_DIR := pdfs
+FIG_DIR := figures
+CALC_DIR := calc
+
+### Here we go
+#
+OUT_PDF:= $(PDF_DIR)/notes.pdf
+
+.PHONY: all
+all: $(OUT_PDF)
+
+### How we do that
+#
+
+## setup main pdf deps as variable that subdirs can add to
+MAIN_PDF_DEPS := bibliography.bib
+
+## Defining common directory recipes
+$(PDF_DIR):
+	mkdir $(PDF_DIR)
+$(FIG_DIR):
+	mkdir -p $(FIG_DIR)
+$(CALC_DIR):
+	mkdir -p $(CALC_DIR)
+
+## Figures
+#
+
+FIGURES := 
+## Making main.pdf and other pdfs
+#
+$(PDF_DIR)/notes.pdf: notes.tex $(MAIN_PDF_DEPS) | $(PDF_DIR) $(FIGURES)
+	$(LATEXMK) $(<F)
+	cp $(@F) $@
+
+### Convenience scripts for tidying tex
+.PHONY: declutter
+declutter:
+	@rm -f *.tdo
+	@rm -f *.run.xml
+	@rm -f *.bbl
+
+.PHONY: tidy
+tidy: declutter
+	@latexmk -c
+.PHONY: clean
+clean: declutter
+	rm -rf $(PDF_DIR)
+	@latexmk -C
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..91be4b1
--- /dev/null
+++ b/README.md
@@ -0,0 +1,3 @@
+# Notes on the lack of convergence for different tau values for sufficiently low T.
+
+Why is this happening?!
diff --git a/bibliography.bib b/bibliography.bib
new file mode 100644
index 0000000..a799f4c
--- /dev/null
+++ b/bibliography.bib
@@ -0,0 +1,245 @@
+@article{Nam1967,
+	doi = {10.1103/physrev.156.470},
+	url = {https://doi.org/10.1103/physrev.156.470},
+	year = {1967},
+	month = apr,
+	publisher = {American Physical Society ({APS})},
+	volume = {156},
+	number = {2},
+	pages = {470--486},
+	author = {Sang Boo Nam},
+	title = {Theory of Electromagnetic Properties of Superconducting and Normal Systems. {I}},
+	journal = {Physical Review}
+}
+
+@book{SolyomV3,
+	doi = {10.1007/978-3-642-04518-9},
+	url = {https://doi.org/10.1007/978-3-642-04518-9},
+	year = {2010},
+	publisher = {Springer Berlin Heidelberg},
+	author = {Jen{\H{o}} S{\'{o}}lyom},
+	title = {Fundamentals of the Physics of Solids},
+	subtitle = {Normal, Broken-Symmetry, and Correlated Systems},
+	volume = {3},
+}
+
+@article{Henkel1999,
+	doi = {10.1007/s003400050823},
+	url = {https://doi.org/10.1007/s003400050823},
+	year = {1999},
+	month = dec,
+	publisher = {Springer Science and Business Media {LLC}},
+	volume = {69},
+	number = {5-6},
+	pages = {379--387},
+	author = {C. Henkel and S. P\"{o}tting and M. Wilkens},
+	title = {Loss and heating of particles in small and noisy traps},
+	journal = {Applied Physics B}
+}
+
+@article{Henkel2006,
+	doi = {10.1007/s00340-006-2219-9},
+	url = {https://doi.org/10.1007/s00340-006-2219-9},
+	year = {2006},
+	month = apr,
+	publisher = {Springer Science and Business Media {LLC}},
+	volume = {84},
+	number = {1-2},
+	pages = {61--68},
+	author = {C. Henkel and K. Joulain},
+	title = {Electromagnetic field correlations near a surface with a nonlocal optical response},
+	journal = {Applied Physics B}
+}
+
+@article{QubitRelax,
+	doi = {10.1103/physreva.86.010301},
+	url = {https://doi.org/10.1103/physreva.86.010301},
+	year = {2012},
+	month = jul,
+	publisher = {American Physical Society ({APS})},
+	volume = {86},
+	number = {1},
+	author = {Luke S. Langsjoen and Amrit Poudel and Maxim G. Vavilov and Robert Joynt},
+	title = {Qubit relaxation from evanescent-wave Johnson noise},
+	journal = {Physical Review A}
+}
+
+@incollection{Pippard,
+	doi = {10.1016/s0065-2539(08)60130-4},
+	url = {https://doi.org/10.1016/s0065-2539(08)60130-4},
+	year = {1954},
+	publisher = {Elsevier},
+	pages = {1--45},
+	author = {A.B. Pippard},
+	title = {Metallic Conduction at High Frequencies and Low Temperatures},
+	booktitle = {Advances in Electronics and Electron Physics Volume 6}
+}
+
+@article{Churchill2016,
+	doi = {10.1103/physrevb.94.235422},
+	url = {https://doi.org/10.1103/physrevb.94.235422},
+	year = {2016},
+	month = dec,
+	publisher = {American Physical Society ({APS})},
+	volume = {94},
+	number = {23},
+	author = {R. J. Churchill and T. G. Philbin},
+	title = {Electromagnetic reflection,  transmission,  and energy density at boundaries of nonlocal media},
+	journal = {Physical Review B}
+}
+
+@book{AGD,
+	author    = {Abrikosov, A A and Dzyaloshinskii, I and Gorkov, L P and Silverman, Richard A},
+	title     = {Methods of quantum field theory in statistical physics},
+	publisher = {Dover},
+	address   = {New York, NY},
+	year      = {1975},
+}
+
+@article{Zimmermann1991,
+	doi = {10.1016/0921-4534(91)90771-p},
+	url = {https://doi.org/10.1016/0921-4534(91)90771-p},
+	year = {1991},
+	month = nov,
+	publisher = {Elsevier {BV}},
+	volume = {183},
+	number = {1-3},
+	pages = {99--104},
+	author = {W. Zimmermann and E.H. Brandt and M. Bauer and E. Seider and L. Genzel},
+	title = {Optical conductivity of {BCS} superconductors with arbitrary purity},
+	journal = {Physica C: Superconductivity}
+}
+
+@article{Ford1984,
+	doi = {10.1016/0370-1573(84)90098-x},
+	url = {https://doi.org/10.1016/0370-1573(84)90098-x},
+	year = {1984},
+	month = nov,
+	publisher = {Elsevier {BV}},
+	volume = {113},
+	number = {4},
+	pages = {195--287},
+	author = {G.W. Ford and W.H. Weber},
+	title = {Electromagnetic interactions of molecules with metal surfaces},
+	journal = {Physics Reports}
+}
+
+@article{Agarwal1975,
+	doi = {10.1103/physreva.11.230},
+	url = {https://doi.org/10.1103/physreva.11.230},
+	year = {1975},
+	month = jan,
+	publisher = {American Physical Society ({APS})},
+	volume = {11},
+	number = {1},
+	pages = {230--242},
+	author = {G. S. Agarwal},
+	title = {Quantum electrodynamics in the presence of dielectrics and conductors. I. Electromagnetic-field response functions and black-body fluctuations in finite geometries},
+	journal = {Physical Review A}
+}
+
+@article{Nam1967_Part2,
+	doi = {10.1103/physrev.156.487},
+	url = {https://doi.org/10.1103/physrev.156.487},
+	year = {1967},
+	month = apr,
+	publisher = {American Physical Society ({APS})},
+	volume = {156},
+	number = {2},
+	pages = {487--493},
+	author = {Sang Boo Nam},
+	title = {Theory of Electromagnetic Properties of Strong-Coupling and Impure Superconductors. {II}},
+	journal = {Physical Review}
+}
+
+@article{Tenberg2019,
+	doi = {10.1103/physrevb.99.205306},
+	url = {https://doi.org/10.1103/physrevb.99.205306},
+	year = {2019},
+	month = may,
+	publisher = {American Physical Society ({APS})},
+	volume = {99},
+	number = {20},
+	author = {Stefanie B. Tenberg and Serwan Asaad and Mateusz T. M{\k{a}}dzik and Mark A. I. Johnson and Benjamin Joecker and Arne Laucht and Fay E. Hudson and Kohei M. Itoh and A. Malwin Jakob and Brett C. Johnson and David N. Jamieson and Jeffrey C. McCallum and Andrew S. Dzurak and Robert Joynt and Andrea Morello},
+	title = {Electron spin relaxation of single phosphorus donors in metal-oxide-semiconductor nanoscale devices},
+	journal = {Physical Review B}
+}
+
+@article{Kolkowitz2015,
+	doi = {10.1126/science.aaa4298},
+	url = {https://doi.org/10.1126/science.aaa4298},
+	year = {2015},
+	month = jan,
+	publisher = {American Association for the Advancement of Science ({AAAS})},
+	volume = {347},
+	number = {6226},
+	pages = {1129--1132},
+	author = {S. Kolkowitz and A. Safira and A. A. High and R. C. Devlin and S. Choi and Q. P. Unterreithmeier and D. Patterson and A. S. Zibrov and V. E. Manucharyan and H. Park and M. D. Lukin},
+	title = {Probing Johnson noise and ballistic transport in normal metals with a single-spin qubit},
+	journal = {Science}
+}
+
+@book{llv9,
+	place={Oxford},
+	title={Statistical Physics. Part 2},
+	volume={9},
+	publisher={Pergamon Press},
+	author={Lifshitz, Evgenii Mikhailovich. and Pitaevskii, Lev Petrovich.},
+	year={1980}
+}
+
+@book{Tinkham,
+	title={Introduction to Superconductivity},
+	author={Michael Tinkham},
+	edition = 2,
+	isbn={9780486435039},
+	lccn={95022378},
+	series={Dover Books on Physics},
+	year={2004},
+	publisher={Dover Publications},
+	location={Mineola, N.Y.},
+}
+
+@article{Mattis,
+	doi = {10.1103/physrev.111.412},
+	url = {https://doi.org/10.1103/physrev.111.412},
+	year = {1958},
+	month = jul,
+	publisher = {American Physical Society ({APS})},
+	volume = {111},
+	number = {2},
+	pages = {412--417},
+	author = {D. C. Mattis and J. Bardeen},
+	title = {Theory of the Anomalous Skin Effect in Normal and Superconducting Metals},
+	journal = {Physical Review}
+}
+
+@book{FetterWalecka,
+	address = {Boston},
+	author = {Fetter, A. L. and Walecka, J. D.},
+	publisher = {McGraw-Hill},
+	title = {Quantum Theory of Many-Particle Systems},
+	year = 1971
+}
+
+@article{Lindhard,
+	title = {ON THE PROPERTIES OF A GAS OF CHARGED PARTICLES},
+	author = {Lindhard, J},
+	abstractNote = {},
+	doi = {},
+	journal = {Kgl. Danske Videnskab. Selskab Mat.-fys. Medd.},
+	number = 8,
+	volume = 28,
+	year = {1954},
+	month = {1}
+}
+
+@book{LandauLifshitzElectrodynamics,
+	author        = "Landau, Lev Davidovich and Lifshitz, Evgenii Mikhailovich and Pitaevskii, Lev Petrovich",
+	title         = "{Electrodynamics of continuous media; 2nd ed.}",
+	publisher     = "Butterworth",
+	address       = "Oxford",
+	series        = "Course of theoretical physics",
+	year          = "1984",
+	url           = "https://cds.cern.ch/record/712712",
+}
diff --git a/do.sh b/do.sh
new file mode 100644
index 0000000..9d0c9ad
--- /dev/null
+++ b/do.sh
@@ -0,0 +1,18 @@
+#!/usr/bin/env sh
+# Do - The Simplest Build Tool on Earth.
+# Documentation and examples see https://github.com/8gears/do
+
+set -Eeuo pipefail # -e "Automatic exit from bash shell script on error"  -u "Treat unset variables and parameters as errors"
+
+build() {
+   echo "I am ${FUNCNAME[0]}ing"
+   make pdfs/notes.pdf
+}
+
+all() {
+   build
+}
+
+"$@" # <- execute the task
+
+[ "$#" -gt 0 ] || printf "Usage:\n\t./do.sh %s\n" "($(compgen -A function | grep '^[^_]' | paste -sd '|' -))"
diff --git a/figures/lukemagnoise.jpg b/figures/lukemagnoise.jpg
new file mode 100644
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diff --git a/notes.tex b/notes.tex
new file mode 100644
index 0000000..c4e32e6
--- /dev/null
+++ b/notes.tex
@@ -0,0 +1,55 @@
+\documentclass{article}
+
+%other packages
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{physics}
+
+\usepackage[
+	style=phys, articletitle=false, biblabel=brackets, chaptertitle=false, pageranges=false, url=true
+]{biblatex}
+
+\usepackage{graphicx}
+\usepackage{todonotes}
+\usepackage{siunitx}
+
+\usepackage{cleveref}
+
+\title{Noise on ewjn mag noise}
+
+\addbibresource{./bibliography.bib}
+
+\graphicspath{{./figures/}}
+
+\newcommand{\vf}{v_{\mathrm{F}}}
+\newcommand{\qf}{q_{\mathrm{F}}}
+
+\begin{document}
+
+\maketitle
+
+The reproduction of the magnetic noise in \cite{QubitRelax} is below, in \cref{fig:lukemag}.
+The important point for reproducing the figure in Luke's paper is that I did not use the expression for $r_s$ there.
+Instead, I used eqs 2.20 and 2.26 in Ford-Weber\cite{Ford1984}:
+
+\begin{align}
+\zeta_s(u) &= 2 i \int_0^\infty \dd{y} \frac{1}{\epsilon_t(\sqrt{u^2 + y^2}) - u^2 - y^2} \\
+r_s(u) &= \frac{\zeta_s(u) - \frac{\pi}{i u}}{\zeta_s(u) + \frac{\pi}{i u}},
+\end{align}
+up to a constant out front which I pulled to outer code.
+
+Additionally, the other important thing is that every parameter in the caption of Luke's figure 3 are are actually in radians per second, except for $\nu$ (I think).
+The collision frequency $\nu$ is the odd one, because in the expression for $\epsilon$, the local limit reduces to the Drude case precisely with $\tau = \frac{1}{\nu}$.
+I was always under the impression that the Drude $\tau$ just carried units of seconds, rather than seconds per radian, but now I'm not sure (there are after all $\tau \omega$ terms which don't look ``unitless'').
+That all implies that $\tau = \left(6 \pi \right)^{-1} \times \SI{e-12}{\s}$.
+
+
+\begin{figure}[htp]
+	\centering
+	\includegraphics[width=\linewidth]{lukemagnoise}
+	\caption{$T_1(z)$, dotted is the nonlocal case and solid is the local case.} \label{fig:lukemag}
+\end{figure}
+
+\printbibliography
+
+\end{document}