Denoising and Extension of Response Functions in the Time Domain

TL;DR

This paper introduces methods to denoise and extend response functions in the time domain, leveraging their causality and positivity properties to improve data quality and spectral analysis in quantum systems.

Contribution

It presents novel techniques for noise reduction and positive extension of response functions based on their intrinsic causal and spectral properties.

Findings

Effective noise reduction in response function data.

Guaranteed positive spectral extensions from finite-time data.

Enhanced accuracy in quantum system response analysis.

Abstract

Response functions of quantum systems, such as electron Green's functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and quantum computing and measured directly in experiment. Response functions are intrinsically causal. In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain. Since response functions define an inner product on a Hilbert space and thereby induce a positive definite function, the properties of this function can be used to reduce noise in measured data and, in equilibrium and steady state, to construct positive definite extensions for data known on finite time intervals, which are then guaranteed to correspond to positive spectra.