Wavepacket dynamics of the nonlinear Harper model

Ng, Gim Seng; Kottos, Tsampikos

doi:10.1103/physrevb.75.205120

Cited by 26 publications

(22 citation statements)

References 42 publications

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“…Although studies of wavepacket spreading in the closed system have shown hints of anomalous diffusion (as opposed to normal diffusion) behaviour at the critical point [45][46][47][48], the exact nature of transport at the critical point…”

Section: Introductionmentioning

confidence: 99%

Anomalous transport in the Aubry-André-Harper model in isolated and open systems

et al. 2018

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We study the high temperature transport behavior of the Aubry-André-Harper (AAH) model, both in the isolated thermodynamic limit and in the open system. At the critical point of the AAH model, we find hints of super-diffusive behavior from the scaling of spread of an initially localized wavepacket. On the other hand, when connected to two baths with different chemical potentials at the two ends, we find that the critical point shows clear sub-diffusive scaling of current with system size. We provide an explanation of this by showing that the current scaling with system-size is entirely governed by the behavior of the single particle eigenfunctions at the boundary sites where baths are attached. We also look at the particle density profile in non-equilibrium steady state of the open system when the two baths are at different chemical potentials. We find that the particle density profile has distinctly different behavior in the delocalized, critical and localized phases of the AAH model. arXiv:1702.05228v3 [cond-mat.mes-hall]

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Section: Introductionmentioning

confidence: 99%

Anomalous transport in the Aubry-André-Harper model in isolated and open systems

et al. 2018

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“…Numerical simulations studying nonlinear dynamics of wave packets have also been performed in the case of quasiperiodic systems [18][19][20][21]. In particular, for exponentially localized linear waves, nonlinearity yields subdiffusive spreading of wave packets as well [20].…”

Section: Introductionmentioning

confidence: 99%

Subdiffusion of nonlinear waves in quasiperiodic potentials

Larcher

Laptyeva²,

Bodyfelt³

et al. 2012

New J. Phys.

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We study the time evolution of wave packets in one-dimensional quasiperiodic lattices which localize linear waves. Nonlinearity (related to twobody 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.

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“…In ultracold gases, thanks to the availability of Feshbach resonances, the interaction between atoms can be changed almost at will, thus allowing for the investigation of the role played by interaction in the transition from diffusion to localization [6]. The effects of interaction have been recently the subject of several theoretical investigations in the case of localization in purely random potentials [7,8,9,10,11,12] and quasi-periodic potentials [13,14,15], but some results are still controversial. It is worth mentioning that the Aubry-Andrè model has been recently implemented also in experiments with diffusion of light in photonic lattices [16].…”

Section: Introductionmentioning

confidence: 99%

Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasiperiodic potentials

2009

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We study the behaviour of an ultracold atomic gas of bosons in a bichromatic lattice, where the weaker lattice is used as a source of disorder. We numerically solve a discretized mean-field equation, which generalizes the one-dimensional Aubry-Andrè model for particles in a quasi-periodic potential by including the interaction between atoms. We compare the results for commensurate and incommensurate lattices. We investigate the role of the initial shape of the wavepacket as well as the interplay between two competing effects of the interaction, namely self-trapping and delocalization. Our calculations show that, if the condensate initially occupies a single lattice site, the dynamics of the interacting gas is dominated by self-trapping in a wide range of parameters, even for weak interaction. Conversely, if the diffusion starts from a Gaussian wavepacket, self-trapping is significantly suppressed and the destruction of localization by interaction is more easily observable.

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Wavepacket dynamics of the nonlinear Harper model

Cited by 26 publications

References 42 publications

Anomalous transport in the Aubry-André-Harper model in isolated and open systems

Anomalous transport in the Aubry-André-Harper model in isolated and open systems

Subdiffusion of nonlinear waves in quasiperiodic potentials

Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasiperiodic potentials

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