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Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices. (English) Zbl 1336.65195

Summary: 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 (\(q \approx 1\)) 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.

MSC:

65P10 Numerical methods for Hamiltonian systems including symplectic integrators
82C44 Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics
65P20 Numerical chaos
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
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