
Seminar "Spectral Problems in Mathematical Physics"
Organizers: Maria Esteban (ParisDauphine), Clotilde Fermanian (Créteil), Mathieu Lewin (Cergy), Stéphane Nonnenmacher (CEA)
Eric Séré (ParisDauphine): "Kink solutions in a simplified model of Polyacetylene"
Monday 15 April 2013, 14:00  15:00
Amphi Darboux
Abstract:
We consider a simplified model of Polyacetylene introduced by Su, Schrieffer and Cheeger in 1979, which belongs to the class of Peierls models at halffilling. 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 KennedyLieb in one direction of the chain, and to the other solution in the other direction.
This is joint work with Mauricio Garcia Arroyo.