Localization in fractal and multifractal media

Abstract

The propagation of waves in highly inhomogeneous media is a problem of interest in multiple fields including seismology, acoustics and electromagnetism. It is also relevant for technological applications such as the design of sound absorbing materials or the fabrication of optically devices for multi-wavelength operation. A paradigmatic example of a highly inhomogeneous media is one in which the density or stiffness has fractal or multifractal properties. We investigate wave propagation in one dimensional media with these features. We have found that, for weak disorder, localization effects do not arrest wave propagation provided that the box fractal dimension D of the density profile is D < 3/2. This result holds for both fractal and multifractal media providing thus a simple universal characterization for the existence of localization in these systems. Moreover we show that our model verifies the scaling theory of localization and discuss practical applications of our results.

4 pages, 5 figures

References in corpus (6)

• Turbulent-Like Behavior of Seismic Time Series
• Lyapunov exponent for the laser speckle potential: a weak disorder expansion
• Differentiable potentials and metallic states in disordered one-dimensional systems
• Fractional derivatives of random walks: Time series with long-time memory
• Lyapunov exponents in 1d disordered system with long-range memory
• Random walk in two-dimensional self-affine random potentials : strong disorder renormalization approach

Cited by in corpus (6)

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• Fractional Stochastic Loewner Evolution and Scaling Curves
• Localization in One-Dimensional Tight-Binding Model with Chaotic Binary Sequences
• Delocalization in One-Dimensional Tight-Binding Models with Fractal Disorder II: Existence of Mobility Edge