Discrete nonlinear Schrödinger equation in complex networks

Details Discrete nonlinear Schrödinger equation in complex networks Discrete nonlinear Schrödinger equation in complex networks

2009-09-17

arxiv.org/abs/0909.3172v2

F.Perakis, G.P.Tsironis, Physics Letters A 375 (2011) 676-679

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 5 figures

Scientific paper

10.1016/j.physleta.2010.11.053

We investigate dynamical aspects of the discrete nonlinear Schr\"{o}dinger equation (DNLS) in finite lattices. Starting from a periodic chain with nearest neighbor interactions, we insert randomly links connecting distant pairs of sites across the lattice. Using localized initial conditions we focus on the time averaged probability of occupation of the initial site as a function of the degree of complexity of the lattice and nonlinearity. We observe that selftrapping occurs at increasingly larger values of the nonlinearity parameter as the lattice connectivity increases, while close to the fully coupled network limit, localization becomes more preferred. For nonlinearity values above a certain threshold we find a reentrant localization transition, viz. localization when the number of long distant bonds is small followed by delocalization and enhanced transport at intermediate bond numbers while close to the fully connected limit localization reappears.

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