Selfconsistent Approximations in Mori's Theory

TL;DR

This paper develops a selfconsistent approximation method within Mori's theory to derive dynamic and static correlations, applying it to spin models and comparing results with established approaches.

Contribution

It introduces a new selfconsistent expansion approach in Mori's theory, linking dynamic equations with mode-mode coupling and static correlations via fluctuation-dissipation theorems.

Findings

Convergence of the expansion is demonstrated for a simple spin model.

Dynamic and static correlations are successfully calculated for a Heisenberg ferromagnet at low temperatures.

Results agree with those obtained from Holstein-Primakoff treatment.

Abstract

The constitutive quantities in Mori's theory, the residual forces, are expanded in terms of time dependent correlation functions and products of operators at $t=0$, where it is assumed that the time derivatives of the observables are given by products of them. As a first consequence the Heisenberg dynamics of the observables are obtained as an expansion of the same type. The dynamic equations for correlation functions result to be selfconsistent nonlinear equations of the type known from mode-mode coupling approximations. The approach yields a neccessary condition for the validity of the presented equations. As a third consequence the static correlations can be calculated from fluctuation-dissipation theorems, if the observables obey a Lie algebra. For a simple spin model the convergence of the expansion is studied. As a further test, dynamic and static correlations are calculated for a Heisenberg ferromagnet at low temperatures, where the results are compared to those of a Holstein Primakoff treatment.