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Analytic Lyapunov exponents in a classical nonlinear field equation

Roberto Franzosi·Raoul Gatto·Giulio Pettini·Marco Pettini
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Abstract

It is shown that the nonlinear wave equation $\partial_t^2ϕ- \partial^2_x ϕ-μ_0\partial_x(\partial_xϕ)^3 =0$, which is the continuum limit of the Fermi-Pasta-Ulam (FPU) beta model, has a positive Lyapunov exponent lambda_1, whose analytic energy dependence is given. The result (a first example for field equations) is achieved by evaluating the lattice-spacing dependence of lambda_1 for the FPU model within the framework of a Riemannian description of Hamiltonian chaos. We also discuss a difficulty of the statistical mechanical treatment of this classical field system, which is absent in the dynamical description.

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Roberto Franzosi, Raoul Gatto, Giulio Pettini, Marco Pettini. 2000-01-03. Analytic Lyapunov exponents in a classical nonlinear field equation. https://doi.org/10.1103/physreve.61.r3299

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