Journal Articles
Permanent URI for this collectionhttps://mro.massey.ac.nz/handle/10179/7915
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Item The crossover from strong to weak chaos for nonlinear waves in disordered systems(EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY, 1/08/2010) Laptyeva TV; Bodyfelt JD; Krimer DO; Skokos C; Flach SWe observe a crossover from strong to weak chaos in the spatiotemporal evolution of multiple-site excitations within disordered chains with cubic nonlinearity. Recent studies have shown that Anderson localization is destroyed, and the wave packet spreading is characterized by an asymptotic divergence of the second moment m2 in time (as t1/3), due to weak chaos. In the present paper, we observe the existence of a qualitatively new dynamical regime of strong chaos, in which the second moment spreads even faster (as t1/2), with a crossover to the asymptotic law of weak chaos at larger times. We analyze the pecularities of these spreading regimes and perform extensive numerical simulations over large times with ensemble averaging. A technique of local derivatives on logarithmic scales is developed in order to quantitatively visualize the slow crossover processes. Copyright © 2010 EPLA.Item Subdiffusion of nonlinear waves in quasiperiodic potentials(IOP PUBLISHING LTD, 1/10/2012) Larcher M; Laptyeva TV; Bodyfelt JD; Dalfovo F; Modugno M; Flach SWe study the time evolution of wave packets in one-dimensional quasiperiodic lattices which localize linear waves. Nonlinearity (related to two-body interactions) has a destructive effect on localization, as observed recently for interacting atomic condensates (Lucioni et al 2011 Phys. Rev. Lett. 106 230403). 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 ∼ t 1/3 and an intermediate m 2 ∼ t 1/2 law. At variance with purely random systems (Laptyeva et al 2010 Europhys. Lett. 91 30001), the fractal gap structure of the linear wave spectrum strongly favours intermediate self-trapping events. Our findings give a new dimension to the theory of wave packet spreading in localizing environments. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.Item Subdiffusion of nonlinear waves in two-dimensional disordered lattices(EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY, 1/06/2012) Laptyeva TV; Bodyfelt JD; Flach SWe perform high-precision computational experiments on nonlinear waves in two-dimensional disordered lattices with tunable nonlinearity. While linear wave packets are trapped due to Anderson localization, nonlinear wave packets spread subdiffusively. Various speculations on the growth of the second moment as t α are tested. Using fine statistical averaging we find agreement with predictions from Flach S., Chem. Phys., 375 (2010) 548, which supports the concepts of strong and weak chaos for nonlinear wave propagation in disordered media. We extend our approach and find potentially long-lasting intermediate deviations due to a growing number of surface resonances of the wave packet. © 2012 EPLA.