Localization--non-ergodic transition in controllable-dimension fractal networks from diffusion-limited aggregation
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910115212296192 |
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| author | Utesov, Oleg I. Andreanov, Alexei Bednarek, Tomasz Siklitskaya, Alexandra Koniakhin, Sergei V. |
| author_facet | Utesov, Oleg I. Andreanov, Alexei Bednarek, Tomasz Siklitskaya, Alexandra Koniakhin, Sergei V. |
| contents | Our study connects the physics of disordered integer-dimensional systems and regular self-similar objects by studying spectral properties of fractal agglomerates with tunable dimension. The latter is controlled by parameter $α$ of the algorithm that generates the agglomerates. We consider the nearest-neighbor tight-binding model on the agglomerates embedded in 2D and 3D, and observe that all eigenstates are localized in the 2D case, whereas in the 3D case, there is a localization--non-ergodic transition upon increasing $α$,i.e., going from sparse to dense fractals: a sub-extensive number of critical states emerge in the spectrum at a certain critical value of $α$. The complex geometry of the agglomerates is also responsible for a peculiar hierarchy of compact localized states and singularities in the density of states, which are typical for ordered fractals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07700 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Localization--non-ergodic transition in controllable-dimension fractal networks from diffusion-limited aggregation Utesov, Oleg I. Andreanov, Alexei Bednarek, Tomasz Siklitskaya, Alexandra Koniakhin, Sergei V. Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics Our study connects the physics of disordered integer-dimensional systems and regular self-similar objects by studying spectral properties of fractal agglomerates with tunable dimension. The latter is controlled by parameter $α$ of the algorithm that generates the agglomerates. We consider the nearest-neighbor tight-binding model on the agglomerates embedded in 2D and 3D, and observe that all eigenstates are localized in the 2D case, whereas in the 3D case, there is a localization--non-ergodic transition upon increasing $α$,i.e., going from sparse to dense fractals: a sub-extensive number of critical states emerge in the spectrum at a certain critical value of $α$. The complex geometry of the agglomerates is also responsible for a peculiar hierarchy of compact localized states and singularities in the density of states, which are typical for ordered fractals. |
| title | Localization--non-ergodic transition in controllable-dimension fractal networks from diffusion-limited aggregation |
| topic | Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2604.07700 |