  We investigate the Loschmidt echo in a one-dimensional spin chain having
Kitaev-type interaction in constant and kicked magnetic fields. The Loschmidt
echo for the initial states having different magnon excitations shows long-time
revivals for smaller chains and has short-time revival peaks for the longer
chains. The system near the critical point shows peculiarly long-time revival
peaks of the Loschmidt echo for relatively larger chains. The presence of a
magnon in the initial state affects the Loschmidt echo revival peaks. The
momentum distribution function exhibits maxima for a few momenta that are
associated with the momentum of the magnon excitation present in the initial
states. The probability maxima decay as O(1/N ) with the system size. For the
Hamiltonian with kicked magnetic fields, the Loschmidt echo depends on the kick
period. For a special kick period, the Loschmidt echo shows no evolution at all
irrespective of the system size.
