  We investigate non-Markovianity measure using two-time correlation functions
for open quantum systems. We define non-Markovianity measure as the difference
between the exact two-time correlation function and the one obtained in the
Markov limit. Such non-Markovianity measure can easily be measured in
experiments. We found that the non-Markovianity dynamics in different time
scale crucially depends on the system-environment coupling strength and other
physical parameters such as the initial temperature of the environment and the
initial state of the system. In particular, we obtain the short-time and
long-time behaviors of non-Markovianity for different spectral densities. We
also find that the thermal fluctuation always reduce the non-Markovian memory
effect. Also, the non-Markovianity measure shows non-trivial initial state
dependence in different time scales.
