From percolation transition to Anderson localization in one-dimensional speckle potentials
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908852807532544 |
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| author | Vrech, Margaux Major, Jan Delande, Dominique Filoche, Marcel Cherroret, Nicolas |
| author_facet | Vrech, Margaux Major, Jan Delande, Dominique Filoche, Marcel Cherroret, Nicolas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16460 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From percolation transition to Anderson localization in one-dimensional speckle potentials Vrech, Margaux Major, Jan Delande, Dominique Filoche, Marcel Cherroret, Nicolas Disordered Systems and Neural Networks Quantum Physics 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. |
| title | From percolation transition to Anderson localization in one-dimensional speckle potentials |
| topic | Disordered Systems and Neural Networks Quantum Physics |
| url | https://arxiv.org/abs/2511.16460 |