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Differentiability of the van der Waals interaction between two atoms

Anapolitanos, Ioannis; Lewin, Mathieu; Roth, Matthias (2019-02), Differentiability of the van der Waals interaction between two atoms. https://basepub.dauphine.fr/handle/123456789/19368

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1902.06683.pdf (300.3Kb)
Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02144016
Date
2019-02
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
33
Metadata
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Author(s)
Anapolitanos, Ioannis
Karlsruher Institut für Technologie [KIT]
Lewin, Mathieu cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Roth, Matthias
Karlsruher Institut für Technologie [KIT]
Abstract (EN)
In this work we improve upon previous results on the expansion of the interaction energy of two atoms. On the one hand we prove the van der Waals-London's law, assuming that only one of the ground state eigenspaces of the atoms is irreducible in an appropriate sense. On the other hand we prove strict monotonicity of the interaction energy at large distances and, under more restrictive assumptions, we provide the leading order of its first two derivatives. The first derivative is interpreted as the force in Physics. Moreover, the estimates of the first two derivatives provide a rigorous proof of the monotonicity and concavity of the interaction energy at large distances.
Subjects / Keywords
van der Waals-London's law; atoms

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