  In this letter, we study the return amplitude, which is the overlap between
the initial state and the time evolved state, in the Sachdev-Ye-Kitaev (SYK)
model. Initial states are taken to be product states in a spin basis. We
numerically study the return amplitude by exactly diagonalizing the
Hamiltonian. We also derive the analytic expression for the return amplitude in
random matrix theory. The SYK results agree with the random matrix expectation.
We also study the time evolution under the different Hamiltonian that describes
the traversable wormholes in projected black holes in the context of
holography. The time evolution now depends on the choice of initial product
states. The results are again explained by random matrix theory. In the
symplectic ensemble cases, we observed an interesting pattern of the return
amplitude where they show the second dip, ramp and plateau like behavior.
