Quantum Macrostatistical Picture of Nonequilibrium Steady States

We apply our quantum macrostatistical treatment of irreversible processes to prove that, in nonequilibrium steady states, (a) the hydrodynamical observables execute a generalised Onsager–Machlup process and (b) the spatial correlations of these observables are generically of long range. The key assumptions behind these results are a nonequilibrium version of Onsager regression hypothesis, together with certain hypotheses of chaoticity and local equilibrium for hydrodynamical fluctuations.     

Non-Markovian Quantum Kinetics and Conservation Laws

A link between memory effects in quantum kinetic equations and nonequilibrium correlations associated with the energy conservation is investigated. In order that the energy be conserved by an approximate collision integral, the one-particle distribution function and the mean interaction energy are treated as independent nonequilibrium state parameters. The density operator method is used to derive a kinetic equation in second-order non-Markovian Born approximation and an evolution equation for the nonequilibrium quasi-temperature which is thermodynamically conjugated to the mean interaction energy. The kinetic equation contains a correlation contribution which exactly cancels the collision term in thermal equilibrium and ensures the energy conservation in nonequilibrium states. Explicit expressions for the entropy production in the non-Markovian regime and the time-dependent correlation energy are obtained.     

Fast-ionic-conductor behavior of driven lattice-gas models

We discuss driven diffusive lattice-gas systems as a model for fast ionic conductors, derive associated hydrodynamic equations and expressions for transport coefficients, and compare mean-field theory, Monte Carlo results and experimental observations. The comparison between model and real behaviours helps to understand some properties of those materials which seem to be characterized by the occurrence of nonequilibrium steady states and phase transitions. In particular, our study suggests the existence in Nature of a novel (nonequilibrium) universality class.     

Higher Order Quantum Onsager Coefficients from Dynamical Invariants

Functionals representing dynamical invariants under unitary quantum dynamics of open systems are used to derive Onsager coefficients for entropy production in irreversible processes if the nonunitary time evolution is determined by quantum dynamical semigroups. The procedure allows a derivation from first principles of the quantum analogue to the classical case.     

Nonequilibrium steady states of stochastic lattice gas models of fast ionic conductors

We investigate theoretically and via computer simulation the stationary nonequilibrium states of a stochastic lattice gas under the influence of a uniform external fieldE. The effect of the field is to bias jumps in the field direction and thus produce a current carrying steady state. Simulations on a periodic 30 × 30 square lattice with attractive nearest-neighbor interactions suggest a nonequilibrium phase transition from a disordered phase to an ordered one, similar to the para-to-ferromagnetic transition in equilibriumE=0. At low temperatures and largeE the system segregates into two phases with an interface oriented parallel to the field. The critical temperature is larger than the equilibrium Onsager value atE=0 and increases with the field. For repulsive interactions the usual equilibrium phase transition (ordering on sublattices) is suppressed. We report on conductivity, bulk diffusivity, structure function, etc. in the steady state over a wide range of temperature and electric field. We also present rigorous proofs of the Kubo formula for bulk diffusivity and electrical conductivity and show the positivity of the entropy production for a general class of stochastic lattice gases in a uniform electric field.Supported in part by National Science Foundation Grant DMR81-14726 and NATO Grant 040.82.Work supported in part by a Lafayette College Junior Faculty Leave Grant.Work supported in part by a Heisenberg fellowship of the Deutsche Forschungsgemeinschaft.     

Entanglement and Classical Correlations in the Quantum Frame

The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones. This leads to a frame in which two kinds of correlations emerge: the classical correlation that is coded in the mixed state of the physical system and a new correlation, to be called probabilistic entanglement, which may occur also at pure states. We examine to what extent this characterization of correlations can be applied to quantum mechanics. Explicit calculations on simple examples outline that a same quantum state can show only classical correlations or only entanglement depending on its statistical content; situations may also arise in which the two kinds of correlations compensate each other.     

Dynamically driven renormalization group

We present a detailed discussion of a novel dynamical renormalization group scheme: the dynamically driven renormalization group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical steady state. The method is based on a real-space renormalization scheme driven by a dynamical steady-state condition which acts as a feedback on the transformation equations. This approach has been applied to open nonlinear systems such as self-organized critical phenomena, and it allows the analytical evaluation of scalling dimensions and critical exponents. Equilibrium models at the critical point can also be considered. The explicit application to some models and the corresponding results are discussed.     

Monte Carlo study of the generalized reaction-diffusion lattice-gas model system

The reaction-diffusion lattice-gas model is an interacting particle system out of equilibrium whose microscopic dynamics is a combination of Glauber (reaction) and Kawasaki (diffusion) processes; the Glauber ratec(s; x) at sitex when the configuration iss satisfies detailed balance at temperatureT, while the Kawasaki ratec(s; x, y) between nearest-neighbor sitesx andy satisfies detailed balance at a different temperatureT. We report on the phase diagram of that system as obtained from a series of Monte Carlo simulations of steady states in two-dimensional lattices with arbitrary values forT,T, and; this generalizes previous analytical and numerical studies for and/orT. When the rates are implemented by the Metropolis algorithm, the system is observed to undergo various types of first- and second-order (nonequilibrium) phase transitions, e.g., one may identify Onsager (equilibrium) as well as Landau (mean-field) types of continuous phase transitions.Dedicated to Joel L. Lebowitz on the occasion of his 60th birthday.     

Quantum dynamical entropies for classical stochastic systems

We compare two proposals for the dynamical entropy of quantum deterministic systems (CNT and AFL) by studying their extensions to classical stochastic systems. We show that the natural measurement procedure leads to a simple explicit expression for the stochastic dynamical entropy with a clear information-theoretical interpretation. Finally, we compare our construction with other recent proposals.     

Prospecting Quantum Correlations and Examining Teleportation Fidelity in a Pair of Coupled Double Quantum Dots System

The topic of improving the ability of quantum systems to retain non-local features and enhance the efficiency of quantum protocols continues. This study delves into the thermal investigation of quantum correlations and teleportation fidelity of a two-qubit teleported state using excess electrons in a coupled double quantum dots system as a quantum channel. The study employs three reliable quantum quantifiers to prospect the resourcefulness and non-classicality of the system. The findings suggest that preserving quantum correlations and optimizing teleportation fidelity require minimizing tunneling coupling and maximizing Coulomb interaction. The study has significant implications for quantum physics and its practical applications in quantum information processing.     

Biased Diffusion with Correlated Noise

The diffusion of hard-core particles subject to a global bias is described by a nonlinear, anisotropic generalization of the diffusion equation with conserved, local noise. Using renormalization group techniques, we analyze the effect of an additional noise term, with spatially long-ranged correlations, on the long-time, long-wavelength behavior of this model. Above an upper critical dimension d _LR, the long-ranged noise is always relevant. In contrast, for d<d _LR, we find a weak noise regime dominated by short-range noise. As the range of the noise correlations increases, an intricate sequence of stability exchanges between different fixed points of the renormalization group occurs. Both smooth and discontinuous crossovers between the associated universality classes are observed, reflected in the scaling exponents. We discuss the necessary techniques in some detail since they are applicable to a much wider range of problems.     

Linear Response Theory for Thermally Driven Quantum Open Systems

This note is a continuation of our recent paper [V. Jakšić Y. Ogata, and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.] where we have proven the Green-Kubo formula and the Onsager reciprocity relations for heat fluxes in thermally driven quantum open systems. In this note we extend the derivation of the Green-Kubo formula to heat and charge fluxes and discuss some other generalizations of the model and results of [V. Jakšić Y. Ogata and C.-A. Pillet, The Green-Kubo formula and Onsager reciprocity relations in quantum statistical mechanics. Commun. Math. Phys. in press.].     

Quantum Thermal Amplifiers with Engineered Dissipation

A three-terminal device, able to control the heat currents flowing through it, is known as a quantum thermal transistor whenever it amplifies two output currents as a response to the external source acting on its third terminal. Several efforts have been proposed in the direction of addressing different engineering options of the configuration of the system. Here, we adhere to the scheme in which such a device is implemented as a three-qubit system that interacts with three separate thermal baths. However, another interesting direction is how to engineer the thermal reservoirs to magnify the current amplification. Here, we derive a quantum dynamical equation for the evolution of the system to study the role of distinct dissipative thermal noises. We compare the amplification gain in different configurations and analyze the role of the correlations in a system exhibiting the thermal transistor effect, via measures borrowed from the quantum information theory.     

Elliptic Quantum Groups and Ruijsenaars Models

We construct symmetric and exterior powers of the vector representation of the elliptic quantum groupsE _Τ,η(slN). The corresponding transfer matrices give rise to various integrable difference equations which could be solved in principle by the nested Bethe ansatz method. In special cases we recover the Ruijsenaars systems of commuting difference operators.     

Peierls Argument and Long-Range Order Behavior of Quantum Lattice Systems with Unbounded Spins

Results on long-range order behavior are obtained for systems in arbitrary dimension (v2) with a wide class of spin–spin long-range interactions, without assuming the reflection positivity property.     

Logarithmic Sobolev inequalities and stochastic Ising models

We use logarithmic Sobolev inequalities to study the ergodic properties of stochastic Ising models both in terms of large deviations and in terms of convergence in distribution.     

Conservation laws in stochastic deposition-evaporation models in one dimension

An infinite number of conservation laws is identified for a stochastic model of deposition and evaporation of trimers on a linear chain. These laws can be encoded into a single nonlocal invariant, the irreducible string, which uniquely lables an exponentially large number of kinetically disconnected sectors of phase space. This enables the number and sizes of sectors to be determined. The effects of conservation laws on some thermodynamic properties are studied.     

Quantum stochastic differential equation for squeezed light

In this paper, the quantum stochastic differential equation (QSDE) is derived which is based on explanatory for interaction of open quantum system with squeezed quantum noise. This equation describes the stochastic evolution of unitary operator and is used to compute the evolution of quantum observable and output field. Our QSDE has complete form with respect to previous QSDE for squeezed light, because it bears three fundamental quantum noises for its evolution and the scattering between quantum channels is included. Meanwhile, when squeezed noise reduces to vacuum noise, our QSDE reveals the famous Hudson-Parthasarathy QSDE. Our equations may have application for quantum network analysis of squeezed noise interferometer for gravitational wave detection.     

Quantum speed limits of a qubit system interacting with a nonequilibrium environment

The speed of evolution of a qubit undergoing a nonequilibrium environment with spectral density of general ohmic form is investigated. First we reveal non-Markovianity of the model, and find that the non-Markovianity quantified by information backflow of Breuer et al. [Phys. Rev. Lett. 103 210401(2009)] displays a nonmonotonic behavior for different values of the ohmicity parameter s in fixed other parameters and the maximal non-Markovianity can be achieved at a specified value s. We also find that the non-Markovianity displays a nonmonotonic behavior with the change of a phase control parameter. Then we further discuss the relationship between quantum speed limit(QSL) time and non-Markovianity of the open-qubit system for any initial states including pure and mixed states. By investigation, we find that the QSL time of a qubit with any initial states can be expressed by a simple factorization law: the QSL time of a qubit with any qubitinitial states are equal to the product of the coherence of the initial state and the QSL time of maximally coherent states,where the QSL time of the maximally coherent states are jointly determined by the non-Markovianity, decoherence factor and a given driving time. Moreover, we also find that the speed of quantum evolution can be obviously accelerated in the wide range of the ohmicity parameter, i.e., from sub-Ohmic to Ohmic and super-Ohmic cases, which is different from the thermal equilibrium environment case.