Subdiffusion of nonlinear waves in quasiperiodic potentials

Abstract

We study the spatio-temporal evolution of wave packets in one-dimensional quasiperiodic lattices which localize linear waves. Nonlinearity (related to two-body interactions) has destructive effect on localization, as recently observed for interacting atomic condensates [Phys. Rev. Lett. 106, 230403 (2011)]. We extend the analysis of the characteristics of the subdiffusive dynamics to large temporal and spatial scales. Our results for the second moment $m_2$ consistently reveal an asymptotic $m_2\sim t^{1/3}$ and intermediate $m_2\sim t^{1/2}$ laws. At variance to purely random systems [Europhys. Lett. 91, 30001 (2010)] the fractal gap structure of the linear wave spectrum strongly favors intermediate self-trapping events. Our findings give a new dimension to the theory of wave packet spreading in localizing environments.

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• Dynamics of spin-orbit coupled Bose-Einstein condensates in a random potential
• Nonlinear lattice waves in heterogeneous media
• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
• Spin-orbit coupled soliton in a random potential
• Quantum chaotic subdiffusion in random potentials
• Classifying transport behavior via current fluctuations in open quantum systems
• Localization of weakly interacting Bose gas in quasiperiodic potential
• Nonlinear Lattice Waves in Random Potentials
• Quantum subdiffusion with two- and three-body interactions
• Modeling the transport of interacting matter-waves in disorder by a non-linear diffusion equation
• Bogoliubov excitations in the quasiperiodic kicked rotor: stability of a kicked condensate and the quasi-insulator-metal transition
• Quench-induced delocalization
• Wave-packet spreading in the disordered and nonlinear Su-Schrieffer-Heeger chain
• Make Slow Fast -- how to speed up interacting disordered matter
• Identification of Anomalous Diffusion Sources by Unsupervised Learning
• Topology of Quantum Grey Soliton in Multi-Component Inhomogeneous Bose-Einstein Condensates
• Spectral description of the dynamics of ultracold interacting bosons in disordered lattices
• Non-linear response of interacting bosons in a quasiperiodic potential
• Slow dissipation and spreading in disordered classical systems: A direct comparison between numerics and mathematical bounds
• Landau instability and mobility edges of the interacting one-dimensional Bose gas in weak random potentials