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Lyapunov exponents as a dynamical indicator of a phase transition

Julien Barre·Thierry Dauxois
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Abstract

We study analytically the behavior of the largest Lyapunov exponent $λ_1$ 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 $λ_1$ as a dynamical indicator close to a phase transition.

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Julien Barre, Thierry Dauxois. 2001-02-19. Lyapunov exponents as a dynamical indicator of a phase transition. https://doi.org/10.1209/epl%2Fi2001-00396-3

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