Scaling of energy spreading in strongly nonlinear disordered lattices

Abstract

To characterize a destruction of Anderson localization by nonlinearity, we study the spreading behavior of initially localized states in disordered, strongly nonlinear lattices. Due to chaotic nonlinear interaction of localized linear or nonlinear modes, energy spreads nearly subdiffusively. Based on a phenomenological description by virtue of a nonlinear diffusion equation we establish a one-parameter scaling relation between the velocity of spreading and the density, which is confirmed numerically. From this scaling it follows that for very low densities the spreading slows down compared to the pure power law.

4 pages, 4 figures

References in corpus (7)

• Anderson Transitions
• Destruction of Anderson localization by a weak nonlinearity
• Universal spreading of wavepackets in disordered nonlinear systems
• Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
• The crossover from strong to weak chaos for nonlinear waves in disordered systems
• Compactons and Chaos in Strongly Nonlinear Lattices
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