2024/08/21 by Scott Lawrence, Lawrence, Scott · 4 citations
Computer Science · Engineering · Medicine · #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Image and Signal Denoising Methods #Medical Imaging Techniques and Applications #Photoacoustic and Ultrasonic Imaging #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2408.11766
openalex publication_date 2024/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.