Discrete nonlinear Schrödinger equation in complex networks

Abstract

We investigate dynamical aspects of the discrete nonlinear Schrödinger 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.

5 pages, 5 figures

References in corpus (3)

• Destruction of Anderson localization by a weak nonlinearity
• Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
• Quantum transport on small-world networks: A continuous-time quantum walk approach

Cited by in corpus (5)

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• Compact Localized States in Engineered Flat-Band $\mathcal{P}\mathcal{T}$ Metamaterials
• Diffusion in infinite and semi-infinite lattices with long-range coupling
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• Exact dynamics for fully connected nonlinear networks