Highly nonlinear solitary waves in chains of ellipsoidal particles

Ngo, Tuan; Khatri, Devvrath; Daraio, Chiara

doi:10.1103/physreve.84.026610

Cited by 28 publications

(9 citation statements)

References 25 publications

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“…In fact, such complicated spatial profiles of probability density are known in quantum systems like billiards or waveguides demonstrating chaotic behavior [4,6,20,21,[25][26][27]. Finally, from Fig.…”

Section: Spin Textures and Spin-charge Separationmentioning

confidence: 94%

“…3 one may notice a developing with the time difference between the distribution of spin and charge, possibly indicating the spin-charge separation in this system. Since the billiard is a simple rectangular, we do not see any specific "scars" in the density usually occurring in the chaotic billiards where chaos appears due to their shape [20,21,26,28]. In our billiard the chaos is generated by the SOC rather than by the geometry [22].…”

Section: Spin Textures and Spin-charge Separationmentioning

confidence: 99%

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Spin chaos manifestation in a driven quantum billiard with spin-orbit coupling

et al. 2013

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The coupling of orbital and spin degrees of freedom is the source of many interesting phenomena. Here, we study the electron dynamics in a quantum billiard driven by a periodic electric field-a mesoscopic rectangular quantum dot-with spin-orbit coupling. We find that the spatial and temporal profiles of the observables demonstrate the transition to chaotic dynamics with qualitative modifications of the power spectra and patterns of probability and spin density. The time dependence of the wavefunctions and spin density indicates spin-charge separation seen in the decay of the spin-charge density correlators. Experimental verification of this spin chaos effect can lead to a better understanding of the interplay between spin and spatial degrees of freedom in mesoscopic systems.

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Section: Spin Textures and Spin-charge Separationmentioning

confidence: 94%

Section: Spin Textures and Spin-charge Separationmentioning

confidence: 99%

Spin chaos manifestation in a driven quantum billiard with spin-orbit coupling

et al. 2013

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“…Most experimental studies on the dynamic response of granular crystals have focused on the elastic response of one-dimensional (1D) and two-dimensional (2D) macroscopic systems, usually composed of 10-800 particles, with diameters in the millimeter-to-centimeter range. Most granular crystals use spherical particles, although an increasing number of recent studies have examined other geometries, including elliptical particles [138], cylindrical particles [99,103], and a combination of different particle shapes [110]. Researchers have used particles made of various materials [136,166,179].…”

Section: Experimental Setupsmentioning

confidence: 99%

Nonlinear coherent structures in granular crystals

Chong

Porter

Kevrekidis

et al. 2017

J. Phys.: Condens. Matter

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The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals, a type of nonlinear metamaterial, exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures -which include traveling solitary waves, dispersive shock waves, and discrete breathers -have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.

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“…( 1) are consequences of the elastic nature of the particle interactions and of the particle geometry [14,15]. Other particle shapes, such as ellipsoids [60] and cylinders [61], can also exhibit Hertzian interactions. The boundary conditions of Eq.…”

Section: A Equations Of Motionmentioning

confidence: 99%

Superdiffusive transport and energy localization in disordered granular crystals

2016

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We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to differ fundamentally from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder-an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements)-and for two types of initial conditions (displacement excitations and velocity excitations). We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics depend strongly on the type of initial condition. In particular, for displacement excitations, the long-time asymptotic behavior of the second moment m̃(2) of the energy has oscillations that depend on the type of disorder, with a complex trend that differs markedly from a power law and which is particularly evident for an Anderson-like disorder. By contrast, for velocity excitations, we find that a standard scaling m̃(2)∼t(γ) (for some constant γ) applies for all three types of disorder. For weakly precompressed (i.e., strongly nonlinear) chains, m̃(2) and the inverse participation ratio P(-1) satisfy scaling relations m̃(2)∼t(γ) and P(-1)∼t(-η), and the dynamics is superdiffusive for all of the cases that we consider. Additionally, when precompression is strong, the inverse participation ratio decreases slowly (with η<0.1) for all three types of disorder, and the dynamics leads to a partial localization around the core and the leading edge of a propagating wave packet. For an Anderson-like disorder, displacement perturbations lead to localization of energy primarily in the core, and velocity perturbations cause the energy to be divided between the core and the leading edge. This localization phenomenon does not occur in the sonic-vacuum regime, which yields the surprising result that the energy is no longer contained in strongly nonlinear waves but instead is spread across many sites. In this regime, the exponents are very similar (roughly γ≈1.7 and η≈1) for all three types of disorder and for both types of initial conditions.

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Highly nonlinear solitary waves in chains of ellipsoidal particles

Cited by 28 publications

References 25 publications

Spin chaos manifestation in a driven quantum billiard with spin-orbit coupling

Spin chaos manifestation in a driven quantum billiard with spin-orbit coupling

Nonlinear coherent structures in granular crystals

Superdiffusive transport and energy localization in disordered granular crystals

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