Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian forms

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.