Scaling properties of energy spreading in nonlinear Hamiltonian two-dimensional lattices

Article, Preprint English OPEN
Mulansky, Mario ; Pikovsky, Arkady (2012)
  • Publisher: AMER PHYSICAL SOC
  • Journal: PHYSICAL REVIEW E (issn: 1539-3755)
  • Related identifiers: doi: 10.1103/PhysRevE.86.056214
  • Subject: Nonlinear Sciences - Chaotic Dynamics | Condensed Matter - Disordered Systems and Neural Networks

In nonlinear disordered Hamiltonian lattices, where there are no propagating phonons, the spreading of energy is of subdiffusive nature. Recently, the universality class of the subdiffusive spreading according to the nonlinear diffusion equation (NDE) has been suggested and checked for one-dimensional lattices. Here, we apply this approach to two-dimensional strongly nonlinear lattices and find a nice agreement of the scaling predicted from the NDE with the spreading results from extensive numerical studies. Moreover, we show that the scaling works also for regular lattices with strongly nonlinear coupling, for which the scaling exponent is estimated analytically. This shows that the process of chaotic diffusion in such lattices does not require disorder.
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