The effect of long-range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on-site potential
Research Center for Astronomy and Applied Mathematics, Academy of Athens,
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
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Published online: 4 October 2018
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.
© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature, 2018