Quantum Ergodicity on large hyperbolic surfaces for local and pseudolocal operators
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910200997347328 |
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| author | Anantharaman, Nalini Saha, Soumyajit |
| author_facet | Anantharaman, Nalini Saha, Soumyajit |
| contents | We prove a quantum ergodicity theorem for sequences of closed hyperbolic surfaces converging to the Poincaré disc in the Benjamini-Schramm sense. Assuming a uniform lower bound on the injectivity radius and a spectral gap, we establish vanishing of quantum variance on fixed spectral windows for a class of observables that contains differential operators and finite-propagation smooth operators. This generalises a result of Le Masson and Sahlsten from scalar observables to both local and 'pseudolocal' operator settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07696 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Ergodicity on large hyperbolic surfaces for local and pseudolocal operators Anantharaman, Nalini Saha, Soumyajit Spectral Theory Mathematical Physics Dynamical Systems Functional Analysis 81Q50, 37D40, 11F72 We prove a quantum ergodicity theorem for sequences of closed hyperbolic surfaces converging to the Poincaré disc in the Benjamini-Schramm sense. Assuming a uniform lower bound on the injectivity radius and a spectral gap, we establish vanishing of quantum variance on fixed spectral windows for a class of observables that contains differential operators and finite-propagation smooth operators. This generalises a result of Le Masson and Sahlsten from scalar observables to both local and 'pseudolocal' operator settings. |
| title | Quantum Ergodicity on large hyperbolic surfaces for local and pseudolocal operators |
| topic | Spectral Theory Mathematical Physics Dynamical Systems Functional Analysis 81Q50, 37D40, 11F72 |
| url | https://arxiv.org/abs/2605.07696 |