2012/03/15 by Alexander V. Milovanov, A. V. Milovanov, Milovanov, A. V. +3
Computer Science · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum chaos and dynamical systems #cond-mat.dis-nn
paper · pdf · doi:10.48550/arxiv.1203.3981
6 pages, 1 figure
arxiv created 2012/03/15 · openalex publication_date 2012/03/15 · arxiv updated 2012/03/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Localization-delocalization transition in a discrete Anderson nonlinear Schrödinger equation with disorder is shown to be a critical phenomenon - similar to a percolation transition on a disordered lattice, with the nonlinearity parameter thought as the control parameter. In vicinity of the critical point the spreading of the wave field is subdiffusive in the limit t→+∞. The second moment grows with time as a powerlaw ∝ tα, with α exactly 1/3. This critical spreading finds its significance in some connection with the general problem of transport along separatrices of dynamical systems with many degrees of freedom and is mathematically related with a description in terms fractional derivative equations. Above the delocalization point, with the criticality effects stepping aside, we find that the transport is subdiffusive with α= 2/5 consistently with the results from previous investigations. A threshold for unlimited spreading is calculated exactly by mapping the transport problem on a Cayley tree.