This study is concernedwith destruction of Anderson localization by a nonlinearity of the power-law type. We suggest using a nonlinear Schrödinger model with random potential on a lattice that quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. For super-quadratic nonlinearity the borderline spreading corresponds to diffusion processes on finite clusters. We have proposed an analytical method to predict and explain such transport processes. Our method uses a topological approximation of the nonlinear Anderson model and, if the exponent of the power nonlinearity is either integer or half-integer, will yield the wanted value of the transport exponent via a triangulation procedure in an Euclidean mapping space. A kinetic picture of the transport arising from these investigations uses a fractional extension of the diffusion equation to fractional derivatives over the time, signifying non-Markovian dynamics with algebraically decaying time correlations.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Computational Mechanics
- Discrete Mathematics and Combinatorics
- Control and Optimization
Milovanov, A. V., & Iomin, A. (2015). Topology of delocalization in the nonlinear Anderson model and anomalous diffusion on finite clusters. Discontinuity, Nonlinearity, and Complexity, 4(2), 151 - 162. https://doi.org/10.5890/DNC.2015.06.003