Statistics of wave interactions in nonlinear disordered systems

Krimer, Dmitry O.; Flach, Sergej

doi:10.1103/physreve.82.046221

Cited by 50 publications

(94 citation statements)

References 33 publications

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“…The second important quantity which enters (18) through the definition of R ν,n in (17) are the overlap integrals I ν,n . Much less is known about these matrix elements (however see [31]). It is instructive to mention that the same overlap integrals play a crucial role when estimating the localization length of two interacting particles (e.g.…”

Section: Beyond the Secular Normal Formmentioning

confidence: 99%

Nonlinear Lattice Waves in Random Potentials

Flach

2015

Nonlinear Optical and Atomic Systems

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Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field. We will discuss recent advances in the dynamics of nonlinear lattice waves in random potentials. In the absence of nonlinear terms in the wave equations, Anderson localization is leading to a halt of wave packet spreading. Nonlinearity couples localized eigenstates and, potentially, enables spreading and destruction of Anderson localization due to nonintegrability, chaos and decoherence. The spreading process is characterized by universal subdiffusive laws due to nonlinear diffusion. We review extensive computational studies for one-and two-dimensional systems with tunable nonlinearity power. We also briefly discuss extensions to other cases where the linear wave equation features localization: Aubry-Andre localization with quasiperiodic potentials, Wannier-Stark localization with dc fields, and dynamical localization in momentum space with kicked rotors.

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Section: Beyond the Secular Normal Formmentioning

confidence: 99%

Nonlinear Lattice Waves in Random Potentials

Flach

2015

Nonlinear Optical and Atomic Systems

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“…I determines the effective strength of coupling between different modes. 31 In the disorder-free limit, I can be calculated explicitly for a chain of size N . The coupling between dispersive band modes is subject to the selection rule k + k 1 − k 2 − k 3 = 2πn, where n is an integer, while the overlap between flat band states vanishes because they all occupy different lattice sites.…”

Section: Dynamicsmentioning

confidence: 99%

Flat band states: Disorder and nonlinearity

et al. 2013

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We study the critical behavior of Anderson localized modes near intersecting flat and dispersive bands in the quasi-one-dimensional diamond ladder with weak diagonal disorder W . The localization length ξ of the flat band states scales with disorder as ξ ∼ W −γ , with γ ≈ 1.3, in contrast to the dispersive bands with γ = 2. A small fraction of dispersive modes mixed with the flat band states is responsible for the unusual scaling. Anderson localization is therefore controlled by two different length scales. Nonlinearity can produce qualitatively different wave spreading regimes, from enhanced expansion to resonant tunneling and self-trapping.

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“…Since m 2 has the units of a square distance, a localization volume in one dimension is defined proportional to √ m 2 [30].…”

Section: Localized Wave Modelsmentioning

confidence: 99%

Decohering localized waves

2013

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In the absence of confinement localization of waves takes place due to randomness or nonlinearity and relies on their phase coherence. We quantitatively probe the sensitivity of localized wave packets to random phase fluctuations and confirm the necessity of phase coherence for localization. Decoherence resulting from a dynamical random environment leads to diffusive spreading and destroys linear and nonlinear localization. We find that maximal spreading is achieved for optimal phase fluctuation characteristics which is a consequence of the competition between diffusion due to decoherence and ballistic transport within the mean free path distance.

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Statistics of wave interactions in nonlinear disordered systems

Cited by 50 publications

References 33 publications

Nonlinear Lattice Waves in Random Potentials

Nonlinear Lattice Waves in Random Potentials

Flat band states: Disorder and nonlinearity

Decohering localized waves

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