  One-spin and two-spin in a thermodynamic limit spin-1/2 chain as open quantum
systems are considered. The dynamics of system is generated by XX Heisenberg
interaction and three-spin interaction (TSI) among all the nearest three spins
in the chain. Two variety Hamiltonians of the three-spin interaction are
considered. Using the fermionization technique and calculating the trace
distance, non-Markovianity as a function of the TSI is evaluated, and the
results for the two different open quantum systems are compared. In addition,
the time behavior of the probability amplitudes are studied. The results show
that if all probability amplitudes except one of them will almost vanish after
some time, the dynamics of the open quantum system will be Markovian. In the
non-Markovian dynamics, more than one of the probability amplitudes fluctuate
in time and will never reach zero value.
