Regular Bohr-Sommerfeld rules for non-self-adjoint Berezin--Toeplitz operators and complex Lagrangian states
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915278956265472 |
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| author | Deleporte, Alix Floch, Yohann Le |
| author_facet | Deleporte, Alix Floch, Yohann Le |
| contents | We describe the eigenvalues and eigenvectors of real-analytic, non-self-adjoint Berezin--Toeplitz operators, up to exponentially small error, on complex one-dimensional compact manifolds, under the hypothesis of regularity of the energy levels. These results form a complex version of the Bohr-Sommerfeld quantization conditions; they hold under a hypothesis that the skew-adjoint part is small but can be of principal order with respect to the semiclassical parameter.
To this end, we develop a calculus of Fourier Integral Operators and Lagrangian states associated with complex Lagrangians; these tools are of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regular Bohr-Sommerfeld rules for non-self-adjoint Berezin--Toeplitz operators and complex Lagrangian states Deleporte, Alix Floch, Yohann Le Spectral Theory Mathematical Physics Symplectic Geometry 81Q20, 35P10, 35P20, 81Q12, 81S10 We describe the eigenvalues and eigenvectors of real-analytic, non-self-adjoint Berezin--Toeplitz operators, up to exponentially small error, on complex one-dimensional compact manifolds, under the hypothesis of regularity of the energy levels. These results form a complex version of the Bohr-Sommerfeld quantization conditions; they hold under a hypothesis that the skew-adjoint part is small but can be of principal order with respect to the semiclassical parameter. To this end, we develop a calculus of Fourier Integral Operators and Lagrangian states associated with complex Lagrangians; these tools are of independent interest. |
| title | Regular Bohr-Sommerfeld rules for non-self-adjoint Berezin--Toeplitz operators and complex Lagrangian states |
| topic | Spectral Theory Mathematical Physics Symplectic Geometry 81Q20, 35P10, 35P20, 81Q12, 81S10 |
| url | https://arxiv.org/abs/2504.00965 |