The effect of long-range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on-site potential

Abstract

The study investigates how long‑range interactions (LRI) influence the dynamics and statistical behavior of one‑dimensional Hamiltonian lattices with on‑site potentials—specifically the Klein–Gordon (KG) and Gorbach–Flach (GF) models. Under LRI, single‑site excitations result in low‑dimensional dynamics described by an undamped Duffing oscillator. Maximal Lyapunov exponents scale with system size N as N^−0.12 (KG) and N^−0.27 (GF), suggesting a movement toward integrability in the thermodynamic limit. Moreover, momentum distributions under LRI deviate markedly from Gaussian statistics typical in FPU‑like systems.