NON-ERGODICITY OF PHASE FUNCTIONS IN CERTAIN SYSTEMS

A lower bound is obtained for the time average of the autocorrelation function of a phase function X(q1,...,Pn), defined for canonical ensembles of classical systems. This lower bound is expressed in terms of averages involving constants of the motion of the systems considered. It is shown that the inequality derived may be used to establish that, for certain systems, a given phase function is not ergodic. The quantum- statistical mechanical version of these results is discussed. As an example it is shown that the z component of the magnetization is not ergodic in the X-Y model of a linear chain of spins 1 2. © 1969.