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

Antonopoulos, CG and Bountis, T and Drossos, L (2015) 'Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices.' Applied Numerical Mathematics, 104. pp. 110-119. ISSN 0168-9274


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© 2015 IMACS 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.

Item Type: Article
Additional Information: 13 pages, 5 figures, published in Applied Numerical Mathematics. arXiv admin note: text overlap with arXiv:1312.5102
Uncontrolled Keywords: Complex statistics; Multi-dimensional maps; McMillan map; Klein-Gordon disordered Hamiltonian; Chaotic and diffusive motion; q-Gaussians; Tsallis entropy
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 20 Oct 2015 13:15
Last Modified: 18 Aug 2022 11:38

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