Analytic Lyapunov exponents in a classical nonlinear field equation

Details Analytic Lyapunov exponents in a classical nonlinear field equation Analytic Lyapunov exponents in a classical nonlinear field equation

2000-01-03

arxiv.org/abs/cond-mat/0001019v1

Phys.Rev. E61 (2000) 3299-3302

Physics

Condensed Matter

Statistical Mechanics

4 pages, 1 figure

Scientific paper

10.1103/PhysRevE.61.R3299

It is shown that the nonlinear wave equation $\partial_t^2\phi - \partial^2_x \phi -\mu_0\partial_x(\partial_x\phi)^3 =0$, 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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