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Pierre-Francois Loos 2020-07-23 15:38:38 +02:00
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RapportStage/Rapport.tex
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\textbf{\huge Pertubation theories in the complex plane}
\textbf{\huge Pertubation theory in the complex plane}
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\textbf{Abstract} : \it In this work, we explore the description of quantum chemistry in the complex plane. We see that the physics of the system can be connected to the position of the energy singularities in the complex plane. After a brief presentation of the fundamental notions of quantum chemistry and perturbation theory in the complex plane, we perform an historical review of the researches that have been done on the physic of singularities. Then we connect all those points of view on this problem using the spherium model (i.e., two opposite-spin electrons restricted to remain on the surface of a sphere of radius $R$) as a theoretical playground. In particular, we explore the effects of symmetry breaking of the wave functions on the singularity structure.
\textbf{Abstract} : \it In this work, we explore the extension of quantum chemistry in the complex plane. We observe that the physics of a quantum system is intimately connected to the position of the energy singularities in the complex plane. After a brief presentation of the fundamental notions of quantum chemistry and perturbation theory in the complex plane, we provide a historical overview of the various research activities that have been performed on the physic of singularities. Then we connect and further discuss these different aspects using the spherium model (i.e., two opposite-spin electrons restricted to remain on the surface of a sphere) as a theoretical playground. In particular, we explore various perturbative partitioning strategies and the effects of symmetry breaking on the singularity structure of the electronic energy. This provides fundamental insights on the location of these singularities in the complex plane (that one calls exceptional points) and, specifically, on the magnitude of the radius of convergence associated with the perturbative treatment.
}
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\textbf{Keywords} : \it Quantum chemistry, Perturbation theory, Spherium, Exceptional points, Symmetry breaking
\textbf{Keywords} : \it quantum chemistry, perturbation theory, complex plane, spherium, exceptional points, radius of convergence, symmetry breaking
} %fin de la commande \parbox des mots clefs
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