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arXiv · 2511.16460

From percolation transition to Anderson localization in one-dimensional speckle potentials

Margaux Vrech·Jan Major·Dominique Delande·Marcel Filoche·Nicolas Cherroret
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Abstract

Classical particles in random potentials typically experience a percolation phase transition, being trapped in clusters of mean size $χ$ that diverges algebraically at a percolation threshold. In contrast, quantum transport in random potentials is controlled by the Anderson localization length, which shows no distinct feature at this classical critical point. Here, we present a comprehensive theoretical analysis of the semi-classical crossover between these two regimes by studying particle propagation in a one-dimensional, red speckle potential, which hosts a percolation transition at its upper bound. As the system deviates from the classical limit, we find that the algebraic divergence of $χ$ continuously connects to a smooth yet non-analytic increase of the localization length. We characterize this behavior both numerically and theoretically using a semi-classical approach. In this crossover regime, the correlated and non-Gaussian nature of the speckle potential becomes essential, causing the standard Dorokhov-Mello-Pereyra-Kumar (DPMK) description for uncorrelated disorder to break down. Instead, we predict the emergence of a bimodal transmission distribution, a behavior normally absent in one dimension, which we capture within our semi-classical analysis. Deep in the quantum regime, the DMPK framework is recovered and the universal features of Anderson localization reappear.

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Margaux Vrech, Jan Major, Dominique Delande, Marcel Filoche, Nicolas Cherroret. 2026-02-26. From percolation transition to Anderson localization in one-dimensional speckle potentials. https://doi.org/10.1088/1367-2630%2Fae4531

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