Prony's method and the connected-moments expansion

TL;DR

This paper demonstrates that Prony's method can fully solve the nonlinear equations of the connected-moments expansion, aiding convergence analysis and enabling calculation of correlation functions in quantum models.

Contribution

It establishes a direct link between Prony's method and the CMX, providing a new approach for analyzing convergence and computing correlation functions in quantum mechanics.

Findings

Prony's method solves the nonlinear CMX equations completely.

Full parameter knowledge aids convergence analysis.

Applicable to simple quantum-mechanical models for correlation functions.

Abstract

We show that Prony's method provides the full solution to the nonlinear equations of the connected--moments expansion (CMX). Knowledge of all the parameters in the CMX ansatz is useful for the analysis of the convergence properties of the approach. Prony's method is also suitable for the calculation of the correlation function for simple quantum--mechanical models.