Walk dimension for light in complex disordered media

Savo, Romolo; Burresi, Matteo; Svensson, Tomas; Vynck, Kevin; Wiersma, Diederik S.

doi:10.1103/physreva.90.023839

Cited by 18 publications

(11 citation statements)

References 45 publications

(70 reference statements)

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“…This behavior could be observed in time resolved experiments which has already been done for quenched systems [30]. By taking the limit k → 0 (large system sizes), we find s ∝ k α with α = 1 leading to an anomalous diffusion equation with a spatial derivative ∆ α/2 which confirms again the presence of Lévy flights [31].…”

Section: Long Time Behavior and Lévy Flightssupporting

confidence: 79%

Signatures of Lévy flights with annealed disorder

Baudouin

Pierrat²,

Eloy³

et al. 2014

Phys. Rev. E

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We present theoretical and experimental results of Lévy flights of light originating from a random walk of photons in a hot atomic vapor. In contrast to systems with quenched disorder, this system does not present any correlations between the position and the step length of the random walk. In an analytical model based on microscopic first principles including Doppler broadening we find anomalous Lévy-type superdiffusion corresponding to a single-step size distribution P (x) ∝ x −(1+α) , with α ≈ 1. We show that this step size distribution leads to a violation of Ohm', as expected for a Lévy walk of independent steps. Furthermore the spatial profile of the transmitted light develops power law tails [T diff (r) ∝ r −3−α ]. In an experiment using a slab geometry with hot rubidium vapor, we measured the total diffuse transmission T diff and the spatial profile of the transmitted light T diff (r). We obtained the microscopic Lévy parameter α under macroscopic multiple scattering conditions paving the way to investigation of Lévy flights in different atomic physics and astrophysics systems.

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Section: Long Time Behavior and Lévy Flightssupporting

confidence: 79%

Signatures of Lévy flights with annealed disorder

Baudouin

Pierrat²,

Eloy³

et al. 2014

Phys. Rev. E

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“…There is an interesting concept to characterize the stochastic transport phenomena by using a spectrum of fractional moments (Castiglione et al, 1999;Metzler and Klafter, 2000;Artuso and Cristadoro, 2003;Sanders and Larralde, 2006;de Anna et al, 2013;Rebenshtok et al, 2014b;Seuront and Stanley, 2014):…”

Section: Mean Squared Displacement and Other Momentsmentioning

confidence: 99%

Lévy walks

2015

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Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The Lévy-walk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, biophysics, and behavioral science demonstrate that this particular type of random walk provides significant insight into complex transport phenomena. This review gives a self-consistent introduction to Lévy walks, surveys their existing applications, including latest advances, and outlines further perspectives.

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“…' 5.1.2. "Power"law"distribution"of"high"refractive"index"clusters"in"1D"photonic"structures" In'some'recent'works' [222,223]'on'the'modelling'of'light'transport'in'Levy'glasses,'the'light' absorption' has' been' correlated' to' the' power' law' of' the' stepJlength' distribution' of' the' light' mean'free'path'in'the'medium. 'The'influence'of''the'power'law'distribution,'of'the'light'free' path'in'the'medium,'on'the'degree'of'superdiffusivity'of'these'materials'is'reported'in'these' studies.…”

Section: Shannon Index Normalized Total Transmissionmentioning

confidence: 99%