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Physica Scripta

Prony's method and the connected-moments expansion

Francisco Marcelo Fernández

Published Jan 31, 2013• 5 citations
Publisher

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 may also be suitable for the calculation of the correlation function for simple quantum-mechanical models.

DOI
10.1088/0031-8949/87/02/025006

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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 may also be suitable for the calculation of the correlation function for simple quantum-mechanical models.
In this paper we have presented a general scheme whereby the method of Padé approximants may be applied to the power series expansion of time dependent correlation functions. It has been demonstrated by actual numerical calculations, using the computer simulated results of Berne and Harp [5], that even a few terms in the power series expansion are capable of reproducing the correlation curves to a fairly large extent. It is pointed out that the method can be extended to higher orders without the introduction of fitting parameters, and without violating the time parity requirements of the Liouville equation. In the final analysis the method is a truly microscopic method since it relies on the microscopic hamiltonian, and the underlying principles are very straightforward. The basic requirements are the spectral moments, but we do not need many of these as the Padé approximants are highly convergent.