2018/01/31 by Helen Christodoulidi, H. Christodoulidi, Anastasios Bountis +2 · 1 citation
Mathematics · Physics and Astronomy · #Breather #Cold Atom Physics and Bose-Einstein Condensates #Duffing equation #Exponent #Gaussian #Hamiltonian (control theory) #Hamiltonian mechanics #Integrable system #Lattice (music) #Lyapunov exponent #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear system #Phase space #Physics #Quantum mechanics #Statistical physics #Strong Light-Matter Interactions #nlin.CD
paper · pdf · doi:10.1140/epjst/e2018-00003-9
10 pages, 6 figures
arxiv created 2018/04/15 · openalex publication_date 2018/09/01 · arxiv updated 2018/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 %: (a) tends to a positive value for KG and grows like ε^(.25) for GF as the energy density ε=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.