  It is shown that the fidelity of the dynamically evolved system with its
earlier time density matrix provides a signature of non-Markovian dynamics.
Also, the fidelity associated with the initial state and the dynamically
evolved state is shown to be larger in the non-Markovian evolution compared to
that in the corresponding Markovian case. Starting from the Kraus
representation of quantum evolution, the Markovian and non-Markovian features
are discerned in its short time structure. These two features are in
concordance with each other and they are illustrated with the help of four
models of interaction of the system with its environment.
