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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2408.11766 |
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| _version_ | 1866911998226202624 |
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| author | Lawrence, Scott |
| author_facet | Lawrence, Scott |
| contents | Various physical quantities -- including real-time response, inclusive cross-sections, and decay rates -- may not be directly determined from Euclidean correlators. They are, however, easily determined from the spectral density, motivating the task of estimating a spectral density from a Euclidean correlator. This spectral reconstruction problem can be written as an ill-posed inverse Laplace transform; incorporating positivity constraints allows one to obtain finite-sized bounds on the region of spectral density functions consistent with the Euclidean data. Expressing the reconstruction problem as a convex optimization problem and exploiting Lagrange duality, bounds on arbitrary integrals of the spectral density can be efficiently obtained from Euclidean data. This paper applies this approach to reconstructing a smeared spectral density and determining smeared real-time evolution. Bounds of this form are information-theoretically complete, in the sense that for any point within the bounds one may find an associated spectral density consistent with both the available Euclidean data and positivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11766 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Model-free spectral reconstruction via Lagrange duality Lawrence, Scott High Energy Physics - Lattice Quantum Physics Various physical quantities -- including real-time response, inclusive cross-sections, and decay rates -- may not be directly determined from Euclidean correlators. They are, however, easily determined from the spectral density, motivating the task of estimating a spectral density from a Euclidean correlator. This spectral reconstruction problem can be written as an ill-posed inverse Laplace transform; incorporating positivity constraints allows one to obtain finite-sized bounds on the region of spectral density functions consistent with the Euclidean data. Expressing the reconstruction problem as a convex optimization problem and exploiting Lagrange duality, bounds on arbitrary integrals of the spectral density can be efficiently obtained from Euclidean data. This paper applies this approach to reconstructing a smeared spectral density and determining smeared real-time evolution. Bounds of this form are information-theoretically complete, in the sense that for any point within the bounds one may find an associated spectral density consistent with both the available Euclidean data and positivity. |
| title | Model-free spectral reconstruction via Lagrange duality |
| topic | High Energy Physics - Lattice Quantum Physics |
| url | https://arxiv.org/abs/2408.11766 |