Volume 55, Number 2, July 2001
|Page(s)||164 - 170|
|Section||Interdisciplinary physics and related areas of science and technology|
|Published online||01 December 2003|
Lyapunov exponents as a dynamical indicator of a phase transition
Laboratoire de Physique, UMR CNRS 5672, Ecole Normale
Supérieure de Lyon
46, allée d'Italie, 69364 Lyon cédex 07, France
Corresponding author: Thierry.Dauxois@ens-lyon.fr
Accepted: 3 May 2001
We study analytically the behavior of the largest Lyapunov exponent for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results to a simple model, proposed for the DNA denaturation, which emphasizes a first-order-like or second-order phase transition depending on the ratio of two length scales: this is an excellent model to characterize as a dynamical indicator close to a phase transition.
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems / 05.70.Fh – Phase transitions: general studies / 02.40.-k – Geometry, differential geometry, and topology
© EDP Sciences, 2001
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