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

Abstract

We examine the role of long--range interactions on the dynamical and statistical properties of two 1D lattices with on--site potentials that are known to support discrete breathers: the Klein--Gordon (KG) lattice which includes linear dispersion and the Gorbach--Flach (GF) lattice, which shares the same on--site potential but its dispersion is purely nonlinear. In both models under the implementation of long--range interactions (LRI) we find that single--site excitations lead to special low--dimensional solutions, which are well described by the undamped Duffing oscillator. For random initial conditions we observe that the maximal Lyapunov exponent $\lambda$ %: (a) tends to a positive value for KG and grows like ${\epsilon }^{(}.25)$ for GF as the energy density $\epsilon =E/N$ increases; (b) saturates to a positive value as the number of particles $N$ increase, scales as $N^{-0.12}$ in the KG model and as $N^{-0.27}$ in the GF with LRI, suggesting in that case an approach to integrable behavior towards the thermodynamic limit. Furthermore, under LRI, their non-Gaussian momentum distributions are distinctly different from those of the FPU model.

10 pages, 6 figures

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Cited by in corpus (1)

• Equilibrium time-correlation functions of the long-range interacting Fermi-Pasta-Ulam model