Application of the Recurrence Relations Method to a many-body model for the study of irreversibility and ergodicity

Abstract

In the context of linear response theory, by means of the Recurrence Relations Method, (RRM), we find exact solutions for the relaxation function and the memory function of an harmonic oscillator chain in thermal equilibrium with one end fixed. We study the analytical properties of these solutions and show that they can exhibit reversible-non-ergodic, irreversible-non-ergodic, and irreversible-ergodic behaviors.