Gaussian Model for Chaotic Instability of Hamiltonian Flows

A general method to describe Hamiltonian chaos in the thermodynamic limit is presented which is based on a model equation independent of the dynamics. This equation is derived from a geometric approach to Hamiltonian chaos recently proposed, and provides an analytic estimate of the largest Lyapunov exponent $\lambda$. The particular case of the Fermi-Pasta-Ulam $\beta$-model Hamiltonian is considered, showing an excellent agreement between the values of $\lambda$ predicted by the model and those obtained with computer simulations of the tangent dynamics.