  We study quasi-particle dynamics in a quasi-periodic Ising model with
temporally fluctuating transverse fields. Specifically, we calculate the
dynamical exponents of the standard deviation of a quasi-particle spreading
under a field chosen randomly from binary values $\pm h$ at every time
interval. We find that the short-time behavior of the dynamical exponents
depends on the interval of the temporally fluctuating fields. We also reveal
how the quasi-particle dynamics affects the relaxation of spin-spin correlation
functions. The dynamics can be explained via the overlap between the
eigenvectors of a Hamiltonian with $\pm h$.
