The Master Ward Identity

In the framework of perturbative quantum field theory (QFT) we propose a new, universal (re)normalization condition (called 'master Ward identity') which expresses the symmetries of the underlying classical theory. It implies for example the field equations, energy-momentum, charge- and ghost-number conservation, renormalized equal-time commutation relations and BRST-symmetry. It seems that the master Ward identity can nearly always be satisfied, the only exceptions we know are the usual anomalies. We prove the compatibility of the master Ward identity with the other (re)normalization conditions of causal perturbation theory, and for pure massive theories we show that the 'central solution' of Epstein and Glaser fulfills the master Ward identity, if the UV-scaling behavior of its individual terms is not relatively lowered. Application of the master Ward identity to the BRST-current of non-Abelian gauge theories generates an identity (called 'master BRST-identity') which contains the information which is needed for a local construction of the algebra of observables, i.e. the elimination of the unphysical fields and the construction of physical states in the presence of an adiabatically switched off interaction.Comment: 73 pages, version to appear in Rev. Math. Phy

Robustness of quantum discord to sudden death

We calculate the dissipative dynamics of two-qubit quantum discord under Markovian environments. We analyze various dissipative channels such as dephasing, depolarizing, and generalized amplitude damping, assuming independent perturbation, in which each qubit is coupled to its own channel. Choosing initial conditions that manifest the so-called sudden death of entanglement, we compare the dynamics of entanglement with that of quantum discord. We show that in all cases where entanglement suddenly disappears, quantum discord vanishes only in the asymptotic limit, behaving similarly to individual decoherence of the qubits, even at finite temperatures. Hence, quantum discord is more robust than the entanglement against to decoherence so that quantum algorithms based only on quantum discord correlations may be more robust than those based on entanglement.Comment: 4 figures, 4 page

Border trees of complex networks

The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real networks were fundamental to stimulate more realistic models and to understand some dynamical processes such as network growth. However, properties related to the network borders (nodes with degree equal to one), one of its most fragile parts, remain little investigated and understood. The border nodes may be involved in the evolution of structures such as geographical networks. Here we analyze complex networks by looking for border trees, which are defined as the subgraphs without cycles connected to the remainder of the network (containing cycles) and terminating into border nodes. In addition to describing an algorithm for identification of such tree subgraphs, we also consider a series of their measurements, including their number of vertices, number of leaves, and depth. We investigate the properties of border trees for several theoretical models as well as real-world networks.Comment: 5 pages, 1 figure, 2 tables. A working manuscript, comments and suggestions welcome

Bilinear and quadratic Hamiltonians in two-mode cavity quantum electrodynamics

In this work we show how to engineer bilinear and quadratic Hamiltonians in cavity quantum electrodynamics (QED) through the interaction of a single driven two-level atom with cavity modes. The validity of the engineered Hamiltonians is numerically analyzed even considering the effects of both dissipative mechanisms, the cavity field and the atom. The present scheme can be used, in both optical and microwave regimes, for quantum state preparation, the implementation of quantum logical operations, and fundamental tests of quantum theory.Comment: 11 pages, 3 figure

Purity as a witness for initial system-environment correlations in open-system dynamics

We study the dynamics of a two-level atom interacting with a Lorentzian structured reservoir considering initial system-environment correlations. It is shown that under strong system-reservoir coupling the dynamics of purity can determine whether there are initial correlations between system and environment. Moreover, we investigate the interaction of two two-level atoms with the same reservoir. In this case, we show that besides determining if there are initial system-environment correlations, the dynamics of the purity of the atomic system allows the identification of the distinct correlated initial states. In addition, the dynamics of quantum and classical correlations is analyzed.Comment: 6 pages, 3 figure

Accelerating networks

Evolving out-of-equilibrium networks have been under intense scrutiny recently. In many real-world settings the number of links added per new node is not constant but depends on the time at which the node is introduced in the system. This simple idea gives rise to the concept of accelerating networks, for which we review an existing definition and -- after finding it somewhat constrictive -- offer a new definition. The new definition provided here views network acceleration as a time dependent property of a given system, as opposed to being a property of the specific algorithm applied to grow the network. The defnition also covers both unweighted and weighted networks. As time-stamped network data becomes increasingly available, the proposed measures may be easily carried out on empirical datasets. As a simple case study we apply the concepts to study the evolution of three different instances of Wikipedia, namely, those in English, German, and Japanese, and find that the networks undergo different acceleration regimes in their evolution.Comment: 12 pages, 8 figure

Nonadiabatic coherent evolution of two-level systems under spontaneous decay

In this paper we extend current perspectives in engineering reservoirs by producing a time-dependent master equation leading to a nonstationary superposition equilibrium state that can be nonadiabatically controlled by the system-reservoir parameters. Working with an ion trapped inside a nonindeal cavity we first engineer effective Hamiltonians that couple the electronic states of the ion with the cavity mode. Subsequently, two classes of decoherence-free evolution of the superposition of the ground and decaying excited levels are achieved: those with time-dependent azimuthal or polar angle. As an application, we generalise the purpose of an earlier study [Phys. Rev. Lett. 96, 150403 (2006)], showing how to observe the geometric phases acquired by the protected nonstationary states even under a nonadiabatic evolution.Comment: 5 pages, no figure