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

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.Comment: 7 pages, 5 eps figures; Discussion on recent characterizations of non-Markovianity included in this versio

Interplay of quantum stochastic and dynamical maps to discern Markovian and non-Markovian transitions

It is known that the dynamical evolution of a system, from an initial tensor product state of system and environment, to any two later times, t1,t2 (t2>t1), are both completely positive (CP) but in the intermediate times between t1 and t2 it need not be CP. This reveals the key to the Markov (if CP) and nonMarkov (if it is not CP) avataras of the intermediate dynamics. This is brought out here in terms of the quantum stochastic map A and the associated dynamical map B -- without resorting to master equation approaches. We investigate these features with four examples which have entirely different physical origins (i) a two qubit Werner state map with time dependent noise parameter (ii) Phenomenological model of a recent optical experiment (Nature Physics, 7, 931 (2011)) on the open system evolution of photon polarization. (iii) Hamiltonian dynamics of a qubit coupled to a bath of $N$ qubits and (iv) two qubit unitary dynamics of Jordan et. al. (Phys. Rev. A 70, 052110 (2004)) with initial product states of qubits. In all these models, it is shown that the positivity/negativity of the eigenvalues of intermediate time dynamical B map determines the Markov/non-Markov nature of the dynamics.Comment: 6 pages, 5 figures, considerably extended version of arXiv:1104.456

Comparison of the quadratic configuration interaction and coupled cluster approaches to electron correlation including the effect of triple excitations

The recently proposed quadratic configuration interaction (QCI) method is compared with the more rigorous coupled cluster (CC) approach for a variety of chemical systems. Some of these systems are well represented by a single-determinant reference function and others are not. The finite order singles and doubles correlation energy, the perturbational triples correlation energy, and a recently devised diagnostic for estimating the importance of multireference effects are considered. The spectroscopic constants of CuH, the equilibrium structure of cis-(NO)2 and the binding energies of Be3, Be4, Mg3, and Mg4 were calculated using both approaches. The diagnostic for estimating multireference character clearly demonstrates that the QCI method becomes less satisfactory than the CC approach as non-dynamical correlation becomes more important, in agreement with a perturbational analysis of the two methods and the numerical estimates of the triple excitation energies they yield. The results for CuH show that the differences between the two methods become more apparent as the chemical systems under investigation becomes more multireference in nature and the QCI results consequently become less reliable. Nonetheless, when the system of interest is dominated by a single reference determinant both QCI and CC give very similar results

Classical Statistics Inherent in a Quantum Density Matrix

A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical underpinning of these correlations. As a byproduct of this analysis, a physical basis of the classical statistical correlations leading to additive entropy in a bipartite system discussed recently by Tsallis et al emerges as inherent classical spin fluctuations. It is found that in this example, the quantum correlations shrink the region of additivity in phase space.Comment: 10 pages, 3 figure