Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices

Chris G. Antonopoulos, Tassos Bountis, Lambros Drossos

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We investigate dynamically and statistically diffusive motion in a chain of linearly coupled 2-dimensional symplectic McMillan maps and find evidence of subdiffusion in weakly and strongly chaotic regimes when all maps of the chain possess a saddle point at the origin and the central map is initially excited. In the case of weak coupling, there is either absence of diffusion or subdiffusion with q>1-Gaussian probability distributions, characterizing weak chaos. However, for large enough coupling and already moderate number of maps, the system exhibits strongly chaotic (q≈1) subdiffusive behavior, reminiscent of the subdiffusive energy spreading observed in a disordered Klein-Gordon Hamiltonian. Our results provide evidence that coupled symplectic maps can exhibit physical properties similar to those of disordered Hamiltonian systems, even though the local dynamics in the two cases is significantly different.
Original languageEnglish
Pages (from-to)110-119
Number of pages10
JournalApplied Numerical Mathematics
Early online date29 Jul 2015
Publication statusPublished - Jun 2016


  • complex statistics
  • multi-dimensional maps
  • McMillan map
  • Klein-Gordon disordered Hamiltonian
  • chaotic and diffusive motion
  • q-Gaussians
  • Tsallis entropy


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