  We consider a coupled top model describing two interacting large spins, which
is studied semiclassically as well as quantum mechanically. This model exhibits
variety of interesting phenomena such as quantum phase transition (QPT),
dynamical transition and excited state quantum phase transitions above a
critical coupling strength. Both classical dynamics and entanglement entropy
reveals ergodic behavior at the center of energy density band for an
intermediate range of coupling strength above QPT, where the level spacing
distribution changes from Poissonian to Wigner-Dyson statistics. Interestingly,
in this model we identify quantum scars as reminiscence of unstable collective
dynamics even in presence of interaction. Statistical properties of such
scarred states deviate from ergodic limit corresponding to random matrix theory
and violate Berry's conjecture. In contrast to ergodic evolution, oscillatory
behavior in dynamics of unequal time commutator and survival probability is
observed as dynamical signature of quantum scar, which can be relevant for its
detection.
