A time-dependent regularization of the Redfield equation

We introduce a new regularization of the Redfield equation based on a replacement of the Kossakowski matrix with its closest positive semidefinite neighbor. Unlike most of the existing approaches, this procedure is capable of retaining the time dependence of the Kossakowski matrix, leading to a completely positive (CP) divisible quantum process. Using the dynamics of an exactly-solvable three-level open system as a reference, we show that our approach performs better during the transient evolution, if compared to other approaches like the partial secular master equation or the universal Lindblad equation. To make the comparison between different regularization schemes independent from the initial states, we introduce a new quantitative approach based on the Choi-Jamiolkoski isomorphism

Nonequilibrium Quantum Phase Transitions in the XY model: comparison of unitary time evolution and reduced density matrix approaches

We study nonequilibrium quantum phase transitions in XY spin 1/2 chain using the $C^*$ algebra. We show that the well-known quantum phase transition at magnetic field $h = 1$ persists also in the nonequilibrium setting as long as one of the reservoirs is set to absolute zero temperature. In addition, we find nonequilibrium phase transitions associated to imaginary part of the correlation matrix for any two different temperatures of the reservoirs at $h = 1$ and $h = h_{\rm c} \equiv|1-\gamma^2|$, where $\gamma$ is the anisotropy and $h$ the magnetic field strength. In particular, two nonequilibrium quantum phase transitions coexist at $h=1$. In addition we also study the quantum mutual information in all regimes and find a logarithmic correction of the area law in the nonequilibrium steady state independent of the system parameters. We use these nonequilibrium phase transitions to test the utility of two models of reduced density operator, namely Lindblad mesoreservoir and modified Redfield equation. We show that the nonequilibrium quantum phase transition at $h = 1$ related to the divergence of magnetic susceptibility is recovered in the mesoreservoir approach, whereas it is not recovered using the Redfield master equation formalism. However none of the reduced density operator approaches could recover all the transitions observed by the $C^*$ algebra. We also study thermalization properties of the mesoreservoir approach.Comment: 25 pages, 10 figure

The interstellar cloud surrounding the Sun: a new perspective

Aims: We offer a new, simpler picture of the local interstellar medium, made of a single continuous cloud enveloping the Sun. This new outlook enables the description of a diffuse cloud from within and brings to light some unexpected properties. Methods: We re-examine the kinematics and abundances of the local interstellar gas, as revealed by the published results for the ultraviolet absorption lines of MgII, FeII, and HI. Results: In contrast to previous representations, our new picture of the local interstellar medium consists of a single, monolithic cloud that surrounds the Sun in all directions and accounts for most of the matter present in the first 50 parsecs around the Sun. The cloud fills the space around us out to about 9 pc in most directions, although its boundary is very irregular with possibly a few extensions up to 20 pc. The cloud does not behave like a rigid body: gas within the cloud is being differentially decelerated in the direction of motion, and the cloud is expanding in directions perpendicular to this flow, much like a squashed balloon. Average HI volume densities inside the cloud vary between 0.03 and 0.1 cm-3 over different directions. Metals appear to be significantly depleted onto grains, and there is a steady increase in depletion from the rear of the cloud to the apex of motion. There is no evidence that changes in the ionizing radiation influence the apparent abundances. Secondary absorption components are detected in 60% of the sight lines. Almost all of them appear to be interior to the volume occupied by the main cloud. Half of the sight lines exhibit a secondary component moving at about -7.2 km/s with respect to the main component, which may be the signature of a shock propagating toward the cloud's interior.Comment: Accepted for publication in Astronomy & Astrophysic

Quantum dynamics of bio-molecular systems in noisy environments

We discuss three different aspects of the quantum dynamics of bio-molecular systems and more generally complex networks in the presence of strongly coupled environments. Firstly, we make a case for the systematic study of fundamental structural elements underlying the quantum dynamics of these systems, identify such elements and explore the resulting interplay of quantum dynamics and environmental decoherence. Secondly, we critically examine some existing approaches to the numerical description of system-environment interaction in the non-perturbative regime and present a promising new method that can overcome some limitations of existing methods. Thirdly, we present an approach towards deciding and quantifying the non-classicality of the action of the environment and the observed system-dynamics. We stress the relevance of these tools for strengthening the interplay between theoretical and experimental research in this field.Comment: Proceedings of the 22nd Solvay Conference in Chemistry on "Quantum Effects in Chemistry and Biology

Self-Consistent Projection Operator Theory in Nonlinear Quantum Optical Systems: A case study on Degenerate Optical Parametric Oscillators

Nonlinear quantum optical systems are of paramount relevance for modern quantum technologies, as well as for the study of dissipative phase transitions. Their nonlinear nature makes their theoretical study very challenging and hence they have always served as great motivation to develop new techniques for the analysis of open quantum systems. In this article we apply the recently developed self-consistent projection operator theory to the degenerate optical parametric oscillator to exemplify its general applicability to quantum optical systems. We show that this theory provides an efficient method to calculate the full quantum state of each mode with high degree of accuracy, even at the critical point. It is equally successful in describing both the stationary limit and the dynamics, including regions of the parameter space where the numerical integration of the full problem is significantly less efficient. We further develop a Gaussian approach consistent with our theory, which yields sensibly better results than the previous Gaussian methods developed for this system, most notably standard linearization techniques.Comment: Comments are welcom

Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping

We propose a method to study the thermodynamic behaviour of small systems beyond the weak coupling and Markovian approximation, which is different in spirit from conventional approaches. The idea is to redefine the system and environment such that the effective, redefined system is again coupled weakly to Markovian residual baths and thus, allows to derive a consistent thermodynamic framework for this new system-environment partition. To achieve this goal we make use of the reaction coordinate mapping, which is a general method in the sense that it can be applied to an arbitrary (quantum or classical and even time-dependent) system coupled linearly to an arbitrary number of harmonic oscillator reservoirs. The core of the method relies on an appropriate identification of a part of the environment (the reaction coordinate), which is subsequently included as a part of the system. We demonstrate the power of this concept by showing that non-Markovian effects can significantly enhance the steady state efficiency of a three-level-maser heat engine, even in the regime of weak system-bath coupling. Furthermore, we show for a single electron transistor coupled to vibrations that our method allows one to justify master equations derived in a polaron transformed reference frame.Comment: updated and improved version; 19 pages incl. 10 figures and 5 pages appendi

Relaxation to persistent currents in a Hubbard trimer coupled to fermionic baths

We consider a ring of fermionic quantum sites, modeled by the Fermi-Hubbard Hamiltonian, in which electrons can move and interact strongly via the Coulomb repulsion. The system is coupled to fermionic cold baths which by the exchange of particles and energy induce relaxation in the system. We eliminate the baths and describe the system effectively by the Lindblad master equations in various versions valid for different coupling parameter regimes. The early relaxation phase proceeds in a universal way, irrespective of the relative couplings and approximations. The system settles down to its low-energy sector and is consecutively well approximated by the Heisenberg model. In the late relaxation, different Lindblad approaches push the system towards different final states with opposite, extreme spin orders, from ferromagenetic to antiferromagnetic. Due to spin frustration in the trimer (a three site ring), degenerate ground states are formed by spin waves (magnons). The system described by the global coherent version of the Lindblad operators relaxes towards the final states carrying directed persistent spin currents. We numerically confirm these predictions.Comment: 24 pages, 14 figure

Stabilizing strongly correlated photon fluids with non-Markovian reservoirs

We introduce a novel frequency-dependent incoherent pump scheme with a square-shaped spectrum as a way to study strongly correlated photons in arrays of coupled nonlinear resonators. This scheme can be implemented via a reservoir of population-inverted two-level emitters with a broad distribution of transition frequencies. Our proposal is predicted to stabilize a non-equilibrium steady state sharing important features with a zero-temperature equilibrium state with a tunable chemical potential. We confirm the efficiency of our proposal for the Bose-Hubbard model by computing numerically the steady state for finite system sizes: first, we predict the occurrence of a sequence of incompressible Mott-Insulator-like states with arbitrary integer densities presenting strong robustness against tunneling and losses. Secondly, for stronger tunneling amplitudes or non-integer densities, the system enters a coherent regime analogous to the superfluid state. In addition to an overall agreement with the zero-temperature equilibrium state, exotic non-equilibrium processes leading to a finite entropy generation are pointed out in specific regions of parameter space. The equilibrium ground state is shown to be recovered by adding frequency-dependent losses. The promise of this improved scheme in view of quantum simulation of the zero temperature many-body physics is highlighted

Quantum trajectory framework for general time-local master equations

The paper was originally submitted as "Interference of Quantum Trajectories". We changed the title after a suggestion of the editorsMaster equations are one of the main avenues to study open quantum systems. When the master equation is of the Lindblad-Gorini-Kossakowski-Sudarshan form, its solution can be "unraveled in quantum trajectories" i.e., represented as an average over the realizations of a Markov process in the Hilbert space of the system. Quantum trajectories of this type are both an element of quantum measurement theory as well as a numerical tool for systems in large Hilbert spaces. We prove that general time-local and trace-preserving master equations also admit an unraveling in terms of a Markov process in the Hilbert space of the system. The crucial ingredient is to weigh averages by a probability pseudo-measure which we call the "influence martingale". The influence martingale satisfies a 1d stochastic differential equation enslaved to the ones governing the quantum trajectories. We thus extend the existing theory without increasing the computational complexity. Quantum trajectory frameworks describe systems weakly coupled to their environment. Here, by including an extra 1D variable in the dynamics, the authors introduce a quantum trajectory framework for time local master equations derived at strong coupling while keeping the computational complexity under control.Peer reviewe