Transparency versus Anderson localization in one-dimensional disordered stealthy hyperuniform layered media

Michael A. Klatt; Paul J. Steinhardt; Salvatore Torquato

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arXiv · 2507.22377

Transparency versus Anderson localization in one-dimensional disordered stealthy hyperuniform layered media

Michael A. Klatt·Paul J. Steinhardt·Salvatore Torquato

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Abstract

We present numerical simulations of disordered stealthy hyperuniform layered media ranging up to 10,000 thin slabs of high-dielectric constant separated by intervals of low dielectric constant that show no apparent evidence of Anderson localization of electromagnetic waves or deviations from transparency for a continuous band of frequencies ranging from zero up to some value $ω_T$. The results are consistent with the strong-contrast formula including its tight upper bound on $ω_T$ and with previous simulations on much smaller systems. We utilize a transfer matrix method to compute the Lyaponov exponents, which we show is a more reliable method for detecting Anderson localization by applying it to a range of systems with common types of disorder known to exhibit localization, such as perturbed periodic lattices. The Lyaponov exponents for these systems with ordinary disorder show clear evidence of localization, in contrast to the cases of perfectly periodically spaced slabs and disordered stealthy hyperuniform layered systems. As with any numerical study, one should be cautious about drawing definitive conclusions. There remains the challenge of determining whether one-dimensional disordered stealthy hyperuniform layered media possess a finite localization length on some scale much larger than our already large system size or, alternatively, are exceptions to the standard Anderson localization theorems.

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Michael A. Klatt, Paul J. Steinhardt, Salvatore Torquato. 2025-07-30. Transparency versus Anderson localization in one-dimensional disordered stealthy hyperuniform layered media. https://arxiv.org/abs/2507.22377

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