Chaotic wave-packet spreading in two-dimensional disordered nonlinear lattices

Manda, Bertin Many; Senyange, B.; Skokos, Ch.

doi:10.1103/physreve.101.032206

Cited by 16 publications

(4 citation statements)

References 45 publications

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“…However, different to what was found in Refs. [4,61,31], for the architected lattice under study, here the slope of Λ does not reach a constant value slope even for the largest possible angular deflection of 45 • . Thus, for the sake of completeness and to be able to compare the results regarding the chaos spreading of the soft architected lattice with other models in the literature, we extend our numerical simulations using even larger initial energies.…”

Section: Strongly Nonlinear Regimementioning

confidence: 78%

“…( 16), is shown to be decreasing in a much slower rate compared to regular dynamics (dashed line). This type of chaotic behavior, where the ftMLE does not reach an asymptotic constant value, has recently attracted much attention and appears to be a particular case of chaos spreading [4,61,31] and it is related to the fact that as the wave-packet spreads, the constant total energy is shared among more sites and consequently the energy per excited site (which plays the role of active nonlinearity strength) decreases. Consequently, the ftMLE which is a global measure of chaos, is also decreasing.…”

Section: Strongly Nonlinear Regimementioning

confidence: 99%

“…[14,16,23] where wave-packet spreading was quantified using both analytical and numerical methods. Moreover, many variations of these 1D lattices have been studied extensively in several works including dynamical regimes ranging from the homogeneous linear to the disordered nonlinear [24,25,26,27,28,29,11,30,31].…”

Section: Introductionmentioning

confidence: 99%

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Wave-packet spreading in disordered soft architected structures

Ngapasare,

Theocharis,

Richoux

et al. 2022

Preprint

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We study the dynamical and chaotic behavior of a disordered one-dimensional elastic mechanical lattice which supports translational and rotational waves. The model used in this work is motivated by the recent experimental results of B. Deng et al., Nat. Commun. 9, 3410 (2018). This lattice is characterized by strong geometrical nonlinearities and the coupling of two degrees-of-freedom (DoFs) per site. Although the linear limit of the structure consists of a linear Fermi-Pasta-Ulam-Tsingou lattice and a linear Klein-Gordon (KG) lattice whose DoFs are uncoupled, by using single site initial excitations on the rotational DoF, we evoke the nonlinear coupling between the system's translational and rotational DoFs. Our results reveal that such coupling induces rich wave-packet spreading behavior in the presence of strong disorder. In the weakly nonlinear regime, we observe energy spreading only due to the coupling of the two DoFs (per site) which is in contrast to what is known for KG lattices with a single DoF per lattice site, where the spreading occurs due to chaoticity. Additionally, for strong nonlinearities, we show that initially localized wave-packets attain near ballistic behavior in contrast to other known models. We also reveal persistent chaos during energy spreading, although its strength decreases in time as quantified by the evolution of the system's finite-time maximum Lyapunov exponent. Our results show that flexible, disordered and strongly nonlinear lattices are a viable platform to study energy transport in combination with multiple DoFs (per site), also present an alternative way to control energy spreading in heterogeneous media.

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Section: Strongly Nonlinear Regimementioning

confidence: 78%

Section: Strongly Nonlinear Regimementioning

confidence: 99%

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Wave-packet spreading in disordered soft architected structures

Ngapasare,

Theocharis,

Richoux

et al. 2022

Preprint

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“…However, the attempt to observe strong chaos and the crossover to weak chaos for the GP lattice failed [15]. The main reason is that the initial norm density a of the wave packet was controlled, but the initial energy density h was fluctuating when choosing and averaging over different disorder realizations [25,26]. As a result, qualitatively different regimes of strong chaos, self-trapping, and Lifshits phases were mixed into one curve.…”

Section: Observation Of Weak and Strong Chaosmentioning

confidence: 99%

Density resolved wave packet spreading in disordered Gross-Pitaevskii lattices

Kati

Flach

2020

SciPost Phys. Core

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We perform novel energy and norm density resolved wave packet spreading studies in the disordered Gross-Pitaevskii (GP) lattice to confine energy density fluctuations. We map the locations of GP regimes of weak and strong chaos subdiffusive spreading in the 2D density control parameter space and observe strong chaos spreading over several decades. We obtain a renormalization of the ground state due to disorder, which allows for a new disorder-induced phase of disconnected insulating puddles of matter due to Lifshits tails. Inside this Lifshits phase, the wave packet spreading is substantially slowed down.

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