Topology of delocalization in the nonlinear Anderson model and anomalous diffusion on finite clusters

A.V. Milovanov, A. Iomin

Research output: Contribution to journalArticle

5 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)151 - 162
Number of pages12
JournalDiscontinuity, Nonlinearity, and Complexity
Issue number2
Publication statusPublished - 2015
Externally publishedYes


All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Computational Mechanics
  • Discrete Mathematics and Combinatorics
  • Control and Optimization

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