We show that the electron transmittivity of single electrons propagating along a 1D wire in the presence of two magnetic impurities is affected by the entanglement between the impurity spins. For suitable values of the electron wave vector, there are two maximally entangled spin states which respectively make the wire completely transparent whatever the electron spin state, or strongly inhibits electron transmission.

We introduce a partial state fidelity approach to quantum phase transitions. We consider a superconducting lattice with a magnetic impurity inserted at its center, and look at the fidelity between partial ͑either one-site or two-site͒ quantum states. In the vicinity of the point of the quantum phase transition, we observe a sudden drop of the fidelity between two one-site partial states corresponding either to the impurity location or its close vicinity. This enables us to identify the on-site magnetization as the order parameter for the phase transition studied. In the case of two-site states, the fidelity reveals the transition point as long as one of the two electron sites is located at the impurity, while the other lies elsewhere in the lattice. We also determine the Uhlmann mixed state geometric phase, recently introduced in the study of the structural change of the system state eigenvectors in the vicinity of the lines of thermal phase transitions, and find it to be trivial, both for one-and two-site partial states, except when an electron site is at the impurity. This means that the system partial state eigenvectors do not contribute significantly to the enhanced state distinguishability around the point of this quantum phase transition. Finally, we use the fidelity to analyze the total amount of correlations contained within a composite system, showing that, even for the smallest one-site states, it features an abrupt quantitative change in the vicinity of the point of the quantum phase transition.

We derive a non-Markovian master equation for the evolution of a class of open quantum systems consisting of quadratic fermionic models coupled to wide-band reservoirs. This is done by providing an explicit correspondence between master equations and non-equilibrium Green's functions approaches. Our findings permit to study non-Markovian regimes characterized by negative decoherence rates. We study the real-time dynamics and the steady-state solution of two illustrative models: a tight-binding and an XY-spin chains. The rich set of phases encountered for the non-equilibrium XY model extends previous studies to the non-Markovian regime.PACS numbers: 05.70. Ln, 05.60.Gg, 03.65.Yz, 42.50.Lc Out-of-equilibrium open quantum systems in contact with thermal reservoirs are fundamentally different from isolated autonomous systems. Thermodynamic gradients, such as temperature and chemical potential differences, may induce a finite flow of particles, energy or spin, otherwise conserved quantities.The interest in out-of-equilibrium processes has been boosted in recent years by considerable experimental progress in the manipulation and control of quantum systems under non-equilibrium conditions in as cold gases [1,2], nano-devices [3,4] and spin [5,6] electronic setups. This renewed attention in non-equilibrium processes has raised a number of new questions, such as the existence of intrinsic out-of-equilibrium phases and phase transitions [7][8][9][10][11], the definition of effective notions of temperature [12][13][14][15][16], universality of dynamics after quenches [17][18][19] and thermalization [20][21][22].Among the set of theoretical tools available to tackle non-equilibrium quantum dynamics [23,24], the Kadanoff-Baym-Keldysh non-equilibrium Green's functions formalism allows for a systematic derivation of the evolution from the microscopic Hamiltonian of the system and its environment. An alternative approach consists on treating open quantum systems with the help of master equations for the reduced density matrix ρ. The formalism is generic as any process describing the evolution of a system and its environment can be effectively described by a master equation of the form [25]where the L 's are a suitable set of jump operators, which, without loss of generality, satisfy tr [L (t)] = 0 and tr L † (t) L (t) = δ , and H is the system's Hamiltonian [26]. The specific form of the L 's is only known for rather specific examples [27][28][29]. To use this approach on a practical level one has to rely on various approximations that restrict its application range [30,31].Trace preservation, which Eq.(1) respects, and positivity are essential in order for ρ (t) to represent a physically allowed density matrix. Generic conditions on L (t) and γ (t) to ensure that the complete positivity of ρ (t) is maintained throughout the evolution are yet unknown [29]. For the case where all decoherence rates are non-negative (γ (t) ≥ 0) positivity can be proven [32,33]. This condition implies that the operator E t,t (ρ) = T e´t t dτ Lτ ...

We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: The Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of superconductivity. In both cases we show that the sudden drop of the mixed state fidelity marks the line of the phase transition. We conduct a detailed analysis of the general case of systems given by mutually commuting Hamiltonians, where the nonanalyticity of the fidelity is directly related to the nonanalyticity of the relevant response functions (susceptibility and heat capacity), for the case of symmetry-breaking transitions. Further, on the case of BCS theory of superconductivity, given by mutually noncommuting Hamiltonians, we analyze the structure of the system's eigenvectors in the vicinity of the line of the phase transition showing that their sudden change is quantified by the emergence of a generically nontrivial Uhlmann mixed state geometric phase.