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

• URL: http://arxiv.org/abs/2511.16460v1
• Date: Thu, 20 Nov 2025 15:26:35 GMT
• Title: From percolation transition to Anderson localization in one-dimensional speckle potentials
• Authors: Margaux Vrech, Jan Major, Dominique Delande, Marcel Filoche, Nicolas Cherroret,
• Abstract summary: Quantum transport in random potentials is controlled by the Anderson localization length, which shows no distinct feature at this classical critical point.<n>We study particle propagation in a one-dimensional, red speckle potential, which hosts a percolation transition at its upper bound.<n>We predict the emergence of a bimodal transmission distribution, a behavior normally absent in one dimension.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 DMPK 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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