81 lines
2.6 KiB
TeX
81 lines
2.6 KiB
TeX
\documentclass{article}
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%other packages
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\usepackage{amsmath}
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\usepackage{amssymb}
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\usepackage{physics}
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\usepackage[
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style=phys, articletitle=false, biblabel=brackets, chaptertitle=false, pageranges=false, url=true
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]{biblatex}
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\usepackage{graphicx}
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\usepackage{todonotes}
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\usepackage{siunitx}
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\usepackage{cleveref}
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\title{Notes on dirty clean limit}
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\addbibresource{./bibliography.bib}
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\graphicspath{{./figures/}}
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\newcommand{\vf}{v_{\mathrm{F}}}
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\newcommand{\qf}{q_{\mathrm{F}}}
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\newcommand{\textforcesc}[1]{\textsc{\MakeLowercase{#1}}}
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\begin{document}
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\maketitle
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\section{Cleanliness dependence of LSW power}
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The power dissipated via \textforcesc{LSW} from Ford and Weber\cite{Ford1984} is at local, quasistatic limit.
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The dirty limit (on the left) matches up with the Mattis-Bardeen case as expected\cite{Mattis}, cf. \cref{fig:namvsmb}.
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This is good because it gives us a bit of confidence in the Nam expressions as we move to the cleaner case.
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However, the clean case looks off in \cref{fig:pvstau}.
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The increase in dissipation as the material gets cleaner doesn't make physical sense.
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This isn't an issue with the full $T_1$ calculations without approximations, as graphed in \cref{fig:t1calc}.
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There are a few differences that could be responsible:
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\begin{itemize}
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\item The \textforcesc{LSW} power calculations are done in the local limit without a cutoff
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\item Local limit vs nonlocal.
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\item Quasistatic issues
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\end{itemize}
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The first doesn't make a ton of sense because the dielectric functions are in the local limit, with $k\rightarrow 0$.
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The cutoff shouldn't actually matter for that.
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The second is on its own has the same issue, seemingly.
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If it were local vs nonlocal, might be able to compensate anyway by just increasing $z$.
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The quasistatic limit seems like the right place to look.
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I don't think there's any reason to assume it would be valid in the superconducting case at this point.
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There may be a more appropriate way of taking the quasistatic limit, somehow with the local limit as well.
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Useful step might be to look at quasistatic limit on its own, without the local assumption.
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And vice-versa.
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\begin{figure}[htp]
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\centering
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\includegraphics[width=12cm]{dirtynamvsmb}
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\caption{The dirty limit of Nam vs Mattis-Bardeen} \label{fig:namvsmb}
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\end{figure}
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\begin{figure}[htp]
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\centering
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\includegraphics[width=12cm]{lswPower-tau}
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\caption{$P_{lsw}$ vs $\tau$} \label{fig:pvstau}
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\end{figure}
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\begin{figure}[htp]
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\centering
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\includegraphics[width=12cm]{fullt1calc}
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\caption{Full $T_1$ calculation} \label{fig:t1calc}
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\end{figure}
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\printbibliography
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\end{document}
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