Analytic Lyapunov exponents in a classical nonlinear field equation
  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. 
Roberto Franzosi (1), Raoul Gatto (2), Giulio Pettini (1), and Marco   Pettini (3) ((1) Dipartimento di Fisica dell'Universi...