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

Christodoulidi, H. and Bountis, A. and Drossos, L. (2018) The effect of long-range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on-site potential. The European Physical Journal Special Topics, 227 (5-6). pp. 563-573. ISSN 1951-6355

Full content URL: http://doi.org/10.1140/epjst/e2018-00003-9

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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.

Keywords:Long-range interactions, Energy localization, Lyapunov exponents, non-Gaussian distributions
Subjects:G Mathematical and Computer Sciences > G121 Mechanics (Mathematical)
G Mathematical and Computer Sciences > G190 Mathematics not elsewhere classified
Divisions:College of Science > School of Mathematics and Physics
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ID Code:37011
Deposited On:16 Sep 2019 09:54

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