2014/05/29 by Alexander V. Milovanov, A. V. Milovanov, Milovanov, A. V. +2
Computer Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Spectroscopy and Quantum Chemical Studies #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.dis-nn #cond-mat.stat-mech #nlin.CD
paper · pdf · doi:10.48550/arxiv.1405.7510
arxiv created 2014/05/29 · openalex publication_date 2014/05/29 · arxiv updated 2014/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This study is concerned with 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.