Non-Markovian Brownian dynamics and nonergodicity.

We report the breaking of ergodicity for a class of generalized, Brownian motion obeying a non-Markovian dynamics being driven by a generalized Langevin equation (GLE). This very feature originates from a vanishing of the effective friction. A novel quantity b (being uniquely determined from the corresponding memory friction kernel gamma(t)of the GLE) is introduced as a parameter that is capable of measuring the strength of ergodicity breaking. The ergodicity breaking is accompanied by a nonunique stationary probability density for the corresponding embedded Markovian dynamics. Differing physical situations for a Brownian, non-Markovian particle dynamics occurring either in free Brownian motion, in a periodic potential, or in a confining potential are elucidated.