Anderson localization as position-dependent diffusion in disordered waveguides

Abstract

We show that the recently developed self-consistent theory of Anderson localization with a position-dependent diffusion coefficient is in quantitative agreement with the supersymmetry approach up to terms of the order of $1/g_0^2$ (with $g_0$ the dimensionless conductance in the absence of interference effects) and with large-scale {\it ab-initio} simulations of the classical wave transport in disordered waveguides, at least for $g_0\gtrsim 0.5$. In the latter case, agreement is found even in the presence of absorption. Our numerical results confirm that in open disordered media, the onset of Anderson localization can be viewed as position-dependent diffusion.

6 pages, 3 figures

References in corpus (18)

• Random-Matrix Theory of Quantum Transport
• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Anderson localization and nonlinearity in one dimensional disordered photonic lattices
• Multiple scattering of classical waves: from microscopy to mesoscopy and diffusion
• Statistics of energy levels and eigenfunctions in disordered systems
• Localization of ultrasound in a three-dimensional elastic network
• Statistical Signatures of Photon Localization
• Observation of the critical regime near Anderson localization of light
• Dynamics of Anderson localization in open 3D media
• Breakdown of Diffusion in Dynamics of Extended Waves in Mesoscopic Media
• Dynamics of weakly localized waves
• Statistical Scattering of Waves in Disordered Waveguides: from Microscopic Potentials to Limiting Macroscopic Statistics
• Microscopic derivation of self-consistent equations of Anderson localization in a disordered medium of finite size
• Supersymmetric field theory of local light diffusion in semi-infinite media
• Effects of resonant tunneling in electromagnetic wave propagation through a polariton gap
• Effect of amplification on conductance distribution of a disordered waveguide
• Comment on "Scaling behavior of classical wave transport in mesoscopic media at the localization transition"

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• Unusual Brownian motion of photons in open absorbing media
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• Numerical study of Anderson localization of terahertz waves in disordered waveguides
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