The evolution of local spin polarization in finite systems involves in
terference phenomena that give rise to quantum dynamical echoes and no
nergodic behavior. We predict the conditions to observe these echoes b
y exploiting the NMR sequences devised by Zhang er al. [Phys. Rev. Let
t. 69, 2149 (1992)], which uses a rare C-13 as the local probe for a d
ipolar coupled H-1 spin system. The nonideality of this probe when tes
ting mesoscopic systems is carefully analyzed revealing the origin of
various striking experimental features.