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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.00650 |
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| _version_ | 1866913175744544768 |
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| author | Aloisio, M. de Oliveira, C. R. Matos, R. Oliveira, D. Pigossi, M. |
| author_facet | Aloisio, M. de Oliveira, C. R. Matos, R. Oliveira, D. Pigossi, M. |
| contents | We develop a deterministic framework showing that a power-law form of semi-uniform localization of eigenfunctions (SULE) imposes strong structural and dynamical constraints on lattice operators. In particular, we prove that power-law SULE yields geometric constraints on localization centers, quantitative bounds on eigenfunction correlators, and power-law localization in the sense of finite moments of the position operator. Conversely, suitable bounds on eigenfunction correlators imply a corresponding form of power-law SULE, establishing a close connection between these notions. This highlights the role of power-law SULE as a structural mechanism governing localization beyond the exponential regime, including features typically associated with Anderson-type models. Our results reveal that power-law localization is intrinsically geometric: the spatial distribution of localization centers directly influences eigenfunction correlators and transport properties. As an application, we obtain power-law localization for long-range lattice operators with Stark-type potentials of sublinear growth whose spectral regime exhibits asymptotically collapsing spectral gaps and quasi-resonant structures, without relying on perturbative methods. Applications to long-range random operators are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00650 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eigenfunction correlators under power-law SULE and localization for lattice operators Aloisio, M. de Oliveira, C. R. Matos, R. Oliveira, D. Pigossi, M. Spectral Theory Mathematical Physics We develop a deterministic framework showing that a power-law form of semi-uniform localization of eigenfunctions (SULE) imposes strong structural and dynamical constraints on lattice operators. In particular, we prove that power-law SULE yields geometric constraints on localization centers, quantitative bounds on eigenfunction correlators, and power-law localization in the sense of finite moments of the position operator. Conversely, suitable bounds on eigenfunction correlators imply a corresponding form of power-law SULE, establishing a close connection between these notions. This highlights the role of power-law SULE as a structural mechanism governing localization beyond the exponential regime, including features typically associated with Anderson-type models. Our results reveal that power-law localization is intrinsically geometric: the spatial distribution of localization centers directly influences eigenfunction correlators and transport properties. As an application, we obtain power-law localization for long-range lattice operators with Stark-type potentials of sublinear growth whose spectral regime exhibits asymptotically collapsing spectral gaps and quasi-resonant structures, without relying on perturbative methods. Applications to long-range random operators are also discussed. |
| title | Eigenfunction correlators under power-law SULE and localization for lattice operators |
| topic | Spectral Theory Mathematical Physics |
| url | https://arxiv.org/abs/2606.00650 |