Eur. Phys. J. Special Topics 227, 563–573 (2018)
https://doi.org/10.1140/epjst/e2018-00003-9

Regular Article

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

¹ Research Center for Astronomy and Applied Mathematics, Academy of Athens, Athens, Greece
² Department of Mathematics, Nazarbayev University, Kabanbay-Batyr 53, 010000 Astana, Republic of Kazakhstan
³ High Performance Computing Systems and Distance Learning Lab, Technological Educational Institute of Western Greece, 26334 Patras, Greece

^a e-mail: anastasios.bountis@nu.edu.kz

Received: 4 January 2018
Published online: 4 October 2018

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 λ 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.