On the spectral relations for multitime correlation functions

TL;DR

This paper develops a rigorous method for deriving spectral relations for multitime correlation functions, focusing on non-ergodic contributions and using multitime temperature Green functions, with applications to three-time correlations.

Contribution

It introduces a comprehensive approach to spectral relations for multitime correlation functions, emphasizing non-ergodic contributions and spectral density reconstruction.

Findings

Spectral relations for multitime correlation functions are derived.

Non-ergodic contributions can be rigorously treated with Green functions.

Spectral densities can be obtained from Green functions for three-time correlations.

Abstract

A general approach for derivation of the spectral relations for the multitime correlation functions is presented. A special attention is paid to the consideration of the non-ergodic (conserving) contributions and it is shown that such contributions can be treated in a rigorous way using multitime temperature Green functions. Representation of the multitime Green functions in terms of the spectral densities and solution of the reverse problem -- finding of the spectral densities from the known Green functions are given for the case of the three-time correlation functions.