Fermi-Pasta-Ulam model with long-range interactions: Dynamics and thermostatistics

We study a long-range–interaction generalisation of the one-dimensional Fermi-Pasta-Ulam (FPU) β-model, by introducing a quartic interaction coupling constant that decays as $1/r^\alpha\ (\alpha \ge 0)$ (with strength characterised by b > 0). In the $\alpha \to\infty$ limit we recover the original FPU model. Through molecular dynamics we show that i) for $\alpha \geq 1$ the maximal Lyapunov exponent remains finite and positive for an increasing number of oscillators N, whereas, for $0 \le \alpha 0$ and $\delta >0$ , in such a way that the q = 1 (BG) behaviour dominates in the $\lim_{N \to\infty} \lim_{t \to\infty}$ ordering, while in the $\lim_{t \to\infty} \lim_{N \to\infty}$ ordering q > 1 statistics prevails