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Loi de van der Waals-London pour les systèmes d'atomes et de molécules relativistes

Abstract : We consider a multiatomic system where the nuclei are assumed to be point charges at fixed positions.Particles interact via Coulomb potential and electrons have relativistic kinetic energy given by (p2+m2)1/2-m.We prove the van der Waals-London law, which states that the interaction energy between neutral atoms decays as the sixth power of the distance |D| between the atoms. We rigorously compute all terms in the binding energy up to order |D|-9 with error term of order O(|D|-10). As intermediate steps we prove exponential decay of eigenfunctions of multiparticle Schrödinger operators with permutation symmetry imposed by the Pauli principle and new estimates of the localization error. In addition we prove the van der Waals-London law for the projected Dirac operator, known as the Brown-Ravenhall operator. In this case we do not calculate the coefficients explicitly and we obtain an error term of order O(|D|-7).
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Michael Hartig. Loi de van der Waals-London pour les systèmes d'atomes et de molécules relativistes. Physique mathématique [math-ph]. Université de Toulon, 2019. Français. ⟨NNT : 2019TOUL0009⟩. ⟨tel-02494777⟩

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