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OK with abstract and intro

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Pierre-Francois Loos 2020-12-05 13:37:23 +01:00
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Cover_Letter/CoverLetter.tex
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@ -19,7 +19,7 @@ In particular, we focus on its mathematical roots and connections with physical
We begin by presenting the fundamental concepts behind non-Hermitian extensions of quantum chemistry into the complex plane, including the Hartree--Fock approximation and
Rayleigh--Schr\"odinger perturbation theory.
We then provide a comprehensive review of the various research that has been performed around the physics of complex singularities in perturbation theory, with a particular focus on M{\o}ller--Plesset theory.
Finally, several resummation techniques are discussedthat can improve energy estimates for both convergent and divergent series, including Pad\'e and quadratic approximants.
Finally, several resummation techniques are discussed that can improve energy estimates for both convergent and divergent series, including Pad\'e and quadratic approximants.
Throughout this review, we present illustrative and pedagogical examples based on the ubiquitous Hubbard dimer at half-filling, reinforcing the amazing versatility of this powerful simplistic model.
Due to the genuine interdisciplinary nature of the present article and its pedagogical aspect, we believe that it will be of interest to a wide audience within the physics and chemistry communities.

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Manuscript/EPAWTFT.tex
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@ -168,7 +168,7 @@ Each of these points is pedagogically illustrated using the Hubbard dimer at hal
% SPIKE THE READER
Perturbation theory isn't usually considered in the complex plane.
Normally it is applied using real numbers as one of very few availabe tools for
describing realistic quantum systems where exact solutions of the Schr\"odinger equation are impossible.\cite{Dirac_1929}
describing realistic quantum systems where exact solutions of the Schr\"odinger equation are impossible \titou{to find?}.\cite{Dirac_1929}
In particular, time-independent Rayleigh--Schr\"odinger perturbation theory\cite{RayleighBook,Schrodinger_1926}
has emerged as an instrument of choice among the vast array of methods developed for this purpose.%
\cite{SzaboBook,JensenBook,CramerBook,HelgakerBook,ParrBook,FetterBook,ReiningBook}