Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.23240 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912793781862400 |
|---|---|
| author | Hayoun, Gabriel Gruzberg, Ilya A. Filoche, Marcel |
| author_facet | Hayoun, Gabriel Gruzberg, Ilya A. Filoche, Marcel |
| contents | We introduce a conceptual reformulation of the Mott-Berezinskiĭ (MB) theory of low-frequency AC conductivity in disordered systems based on localization landscape theory. Instead of assuming uniform localization and fixed hopping distances, transport is described through an effective potential whose geometry encodes the spatial organization and energy-dependent localization of quantum states. Using the associated Agmon metric, we define a generalized Mott scale that replaces the classical hopping length with a geometric criterion set by the disorder landscape. This framework naturally incorporates strong spatial inhomogeneity and yields the AC conductivity directly from the effective potential. The standard MB result is recovered as a limiting case. Our approach extends the conceptual foundation of MB theory to arbitrary disordered media and energies approaching the mobility edge, providing a unified description of AC transport in complex quantum materials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23240 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localization-landscape generalized Mott-Berezinskiĭ formula Hayoun, Gabriel Gruzberg, Ilya A. Filoche, Marcel Disordered Systems and Neural Networks Quantum Physics We introduce a conceptual reformulation of the Mott-Berezinskiĭ (MB) theory of low-frequency AC conductivity in disordered systems based on localization landscape theory. Instead of assuming uniform localization and fixed hopping distances, transport is described through an effective potential whose geometry encodes the spatial organization and energy-dependent localization of quantum states. Using the associated Agmon metric, we define a generalized Mott scale that replaces the classical hopping length with a geometric criterion set by the disorder landscape. This framework naturally incorporates strong spatial inhomogeneity and yields the AC conductivity directly from the effective potential. The standard MB result is recovered as a limiting case. Our approach extends the conceptual foundation of MB theory to arbitrary disordered media and energies approaching the mobility edge, providing a unified description of AC transport in complex quantum materials. |
| title | Localization-landscape generalized Mott-Berezinskiĭ formula |
| topic | Disordered Systems and Neural Networks Quantum Physics |
| url | https://arxiv.org/abs/2512.23240 |