  The evolution of local spin polarization in finite systems involves
interference phenomena that give rise to {\bf quantum dynamical echoes }and
non-ergodic behavior. We predict the conditions to observe these echoes by
exploiting the NMR sequences devised by Zhang et al. [Phys. Rev. Lett. {\bf %
69}, 2149 (1992)], which uses a rare $^{13}$C as {\bf local probe }for a
dipolar coupled $^1$H spin system. The non-ideality of this probe when testing
mesoscopic systems is carefully analyzed revealing the origin of various
striking experimental features.
