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Existence of kink solutions in a discrete model of the polyacetylene molecule

Séré, Eric; Arroyo, Mauricio Garcia (2012), Existence of kink solutions in a discrete model of the polyacetylene molecule. https://basepub.dauphine.fr/handle/123456789/10813

Type
Document de travail / Working paper
External document link
http://hal.archives-ouvertes.fr/hal-00769075
Date
2012
Publisher
Université Paris-Dauphine
Published in
Paris
Pages
20
Metadata
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Author(s)
Séré, Eric
Arroyo, Mauricio Garcia
Abstract (EN)
This paper deals with the proof of the existence of kink states in the discrete model of the polyacetylene molecule . We use ideas from Kennedy and Lieb to study finite, odd chains of polyacetylene, and then we consider the limit as the number of atoms goes to infinity. We show that, after extraction of a subsequence and up to a translation, the energy minimizers of odd chains tend to an infinite vector approaching one of the infinite dimerized states at plus infinity and the other one at minus infinity. This state is called a kink and its existence was strongly suggested in several works in the physical literature, but a mathematical proof was missing, to our knowledge.
Subjects / Keywords
kink solutions; heteroclinic solutions; variational methods; Peierls instability; Peierls model; polyacetylene

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