1207.0721 (Mario Mulansky et al.)

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

Mario Mulansky, Arkady Pikovsky

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.

View original: http://arxiv.org/abs/1207.0721