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\documentclass[a4paper]{letter}
\usepackage[utf8]{inputenc} % why not type "Bézout" with unicode?
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\usepackage[style=phys]{biblatex}
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\signature{
\vspace{-6\medskipamount}
\smallskip
Jaron Kent-Dobias \& Jorge Kurchan
}
\address{
Laboratoire de Physique \\
Ecole Normale Sup\'erieure \\
24 rue Lhomond \\
75005 Paris
}
\begin{document}
\begin{letter}{
Editorial Office\\
Physical Review Letters\\
1 Research Road\\
Ridge, NY 11961
}
\opening{To the editors of Physical Review,}
The subject of `complex landscapes,' which started in the spin-glass
literature, is concerned with functions (landscapes) of many variables having
a multiplicity of minima. Apart from its obvious relevance to glassy systems,
it has found applications in many domains: computer science, ecology,
economics, and biology, to name a few. \footfullcite{Mezard_2009_Information}
In the last few years, a renewed interest has developed in landscapes for
which the variables are complex. There are a couple reasons for this: in
computational physics the `sign problem' is a major obstacle, and a strategy
has emerged to attack it by deforming the sampling space into complex variables.
This is a most natural and promising path, and any progress made will have
game-changing impact in solid state physics and lattice QCD.
\footfullcite{Cristoforetti_2012_New, Scorzato_2016_The} At a more basic
level, following the seminal work of E.~Witten, \footfullcite{Witten_2010_A,
Witten_2011_Analytic} there has been a flurry of activity concerning the very
definition of quantum mechanics, which also requires that one move into the
complex plane.
In these cases, just as in the real case, one needs to understand the structure
of the `landscape,' like the location of saddle points, how they are connected,
and typical questions of `complexity.' However, to the best of our knowledge,
there are no studies extending the methods of the theory of complexity to
complex variables. We believe our paper will open a field that may find
numerous applications and will widen our theoretical view of complexity in
general.
\closing{Sincerely,}
\vspace{1em}
\end{letter}
\end{document}
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