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Seminar "Spectral Problems in Mathematical Physics"
Organizers: Maria Esteban (Paris-Dauphine), Clotilde Fermanian (Créteil), Mathieu Lewin (Cergy), Stéphane Nonnenmacher (CEA)


Eric Séré (Paris-Dauphine): "Kink solutions in a simplified model of Polyacetylene"
Monday 15 April 2013, 14:00 - 15:00
Amphi Darboux



We consider a simplified model of Polyacetylene introduced by Su, Schrieffer and Cheeger in 1979, which belongs to the class of Peierls models at half-filling. In 1987 Kennedy and Lieb studied finite chains and proved that if the number N of nuclei is even, the energy has exactly two minimisers which are periodic of period 2, and are translates of one another by a translation of one unit in the lattice. We study rigorously the case of an odd number of atoms. We prove that if N is odd and converges to infinity, the global minimizer of the energy converges to a "kink" soliton in the infinite chain. This soliton is asymptotic to one of the periodic minimizers found by Kennedy-Lieb in one direction of the chain, and to the other solution in the other direction.

This is joint work with Mauricio Garcia Arroyo.