Model-free spectral reconstruction via Lagrange duality

• URL: http://arxiv.org/abs/2408.11766v1
• Date: Wed, 21 Aug 2024 16:39:37 GMT
• Title: Model-free spectral reconstruction via Lagrange duality
• Authors: Scott Lawrence,
• Abstract summary: Various physical quantities -- including real-time response, inclusive cross-sections, and decay rates -- may not be directly determined from Euclidean correlators. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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