Narrow Results

Using the framework of rigorous algebraic quantum statistical mechanics, we construct the unique nonequilibrium steady state in the isotropic XY chain in which a sample of arbitrary finite size is coupled by a bond coupling perturbation of arbitrary strength to two infinitely extended thermal reservoirs, and we prove that this state is thermodynamically nontrivial. Moreover, extracting the leading second-order contribution to its microscopic entropy production and deriving its entropy production in the van Hove weak coupling regime, we prove that, in the mathematically and physically important XY chain, the van Hove regime reproduces the leading order contribution to the microscopic regime.

With the help of time-dependent scattering theory on the observable algebra of infinitely extended quasifree fermionic chains, we introduce a general class of so-called right mover/left mover states which are inspired by the nonequilibrium steady states for the prototypical nonequilibrium configuration of a finite sample coupled to two thermal reservoirs at different temperatures. Under the assumption of spatial translation invariance, we relate the 2-point operator of such a right mover/left mover state to the asymptotic velocity of the system and prove that the system is thermodynamically nontrivial in the sense that its entropy production rate is strictly positive. Our study of these not necessarily gauge-invariant systems covers and substantially generalizes well-known quasifree fermionic chains and opens the way for a more systematic analysis of the heat flux in such systems.

The conserving sum rules for the electron gas form a set of fundamental and powerful constraints on the description of electronic transport, at any length scale. We examine the particular role of the compressibility sum rule for open mesoscopic conductors, and show that the compressibility in such systems is absolutely invariant under nonequilibrium transport. The compressibility sum rule provides a stringent consistency check on models of mesoscopic conduction.

The effect induced by an environment on a composite quantum system is studied. The model considers the composite system as comprised by a subsystem A coupled to a subsystem B which is also coupled to an external environment. We studied all possible four combinations of subsystems A and B made up with a harmonic oscillator and an upside down oscillator. We analyzed the decoherence suffered by subsystem A due to an effective environment composed by subsystem B and the external reservoir. In all the cases we found that subsystem A decoheres even though it interacts with the environment only through its sole coupling to B. However, the effectiveness of the diffusion depends on the unstable nature of subsystem A and B. Therefore, the role of this degree of freedom in the effective environment is analyzed in detail.

In a quantum measurement setting, it is known that environment-induced decoherence theory describes the emergence of effectively classical features of the quantum system–measuring apparatus composite system when the apparatus is allowed to interact with the environment. In [E. A. Galapon, Europhys. Lett.113, 60007 (2016)], a measurement model is found to have the feature of inducing exact decoherence at a finite time via one internal degree of freedom of the apparatus provided that the apparatus is decomposed into a pointer and an inaccessible probe, with the pointer and the probe being in momentum-limited initial states. However, an issue can be raised against the model: while the factorization method of the time-evolution operator used there is formally correct, it is not completely rigorous due to some unstated conditions on the validity of the factorization in the Hilbert space of the model. Furthermore, no examples were presented there in implementing the measurement scheme in specific quantum systems. The goal of this paper is to re-examine the model and confirm its features independently by solving the von Neumann equation for the joint state of the composite system as a function of time. This approach reproduces the joint state obtained in the original work, leading to the same conditions for exact decoherence and orthogonal pointer states when the required initial conditions on the probe and pointer are imposed. We illustrate the exact decoherence process in the measurement of observables of a spin-1/2 particle and a quantum harmonic oscillator by using the model.

We revisit the problem of quantum diffusion of a particle moving on a lattice with dynamical disorder. Decoherence, essential for the diffusive motion, is introduced via a set of Lindblad operators, known to guarantee per se the positivity, Hermiticity and the trace-class nature of the reduced density matrix, are derived and solved analytically for several transport quantities of interest. For the special Hermitian choice of the Lindblad operators projected onto the lattice sites, we recover several known results, obtained by others, e.g. through the stochastic Liouville equation using phenomenological damping terms for the off-diagonal density-matrix elements. An interesting result that we obtained is for the case of a 1D lattice with static potential bias and a time-harmonic modulation (ac drive) of its transition-matrix element, where the diffusion coefficient shows an oscillatory behavior as function of the drive amplitude and frequency — clearly, a Wannier–Stark ladder signature. The question of dissipation is also briefly discussed.

In this paper, we investigate theoretically a dilute stream of free quantum particles passing through a macroscopic circular aperture of matter-waves and then moving in a space at a finite temperature, taking into account the dissipative coupling with the environment. The portion of particles captured by the detection screen is studied by varying the distance between the aperture and the screen. Depending on the wavelength, the temperature, and the dimension of the aperture, an unusual local valley-peak structure is found in increasing the distance, in contrast to traditional thinking that it decreases monotonically. The underlying mechanism is the nonlocality in the process of decoherence for an individual particle.

Historically cognition was understood as the result of processes occurring solely in the brain. Recently, however, cognitive scientists and philosophers studying "embodied" or "situated" cognition have begun emphasizing the role of the body and environment in which brains are situated, i.e. they view the brain as an "open system". However, these theorists frequently rely on dynamical systems which are traditionally viewed as closed systems. We address this tension by extending the framework of dynamical systems theory. We show how structures which appear in the state space of an embodied agent differ from those that appear in closed systems, and we show how these structures can be used to model representational processes in embodied agents. We focus on neural networks as models of embodied cognition.

A generic architecture for the development and application of software conversion tools exposes the requirements set for appropriate enabling technologies. Extrapolation of this set beyond its satisfaction by existing proprietary technology then exposes the opportunity/need for open interfaces between separate components providing orthogonal dimensions of the overall functionality. Some novel aspects of the solutions considered include retrofitting persistence to an open compiler-compiler, and using the Unix file system as a persistent object store, while in the background the advent of standard interfaces to persistence technology suggests that the overall goal is feasible.

An intelligent information system may be composed of hundreds or thousands of entities each of which may possess some part of the overall knowledge of an organization. In such an environment there is a need for these entities to communicate in order to share knowledge and to cooperate in accomplishing organizational activities. In this paper we propose an architecture for modelling intelligent information systems and discuss how this architecture supports the communication of knowledge in such information systems.

Using the weak coupling limit as a quantum functional central limit (in the sense of Accardi, Frigerio and Lu), we give a quantum Markovian description of the open XY-model, followed by the large-N limit. The treatment is noteworthy for the fact that the harmonic decomposition of the stochastic dynamics is not that of the free evolution, but rather arises from the macroscopic variables being studied. We conclude with a simple Hilbert module formulation of the dynamics.

In this paper we use the stochastic limit approach as a tool to discuss the open BCS model of low temperature superconductivity. We also briefly discuss the role of a second reservoir interacting with the first one (but not with the system) in the computation of the critical temperature corresponding to the transition from a normal to a superconducting phase.

We show that a suitably engineered external non-Gaussian noise can entangle a class of initially separable, polarized two-photon coherent states.

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we solve in the asymptotic long-time regime the master equation for two independent harmonic oscillators interacting with an environment. We give a description of the continuous-variable asymptotic entanglement in terms of the covariance matrix of the considered subsystem for an arbitrary Gaussian input state. Using Peres–Simon necessary and sufficient condition for separability of two-mode Gaussian states, we show that for certain classes of environments the initial state evolves asymptotically to an entangled equilibrium bipartite state, while for other values of the coefficients describing the environment, the asymptotic state is separable. We calculate also the logarithmic negativity characterizing the degree of entanglement of the asymptotic state.

We provide a microscopic derivation for the non-Markovian master equation for an atom-cavity system with cavity losses and show that they can induce population trapping in the atomic excited state, when the environment outside the cavity has a non-flat spectrum. Our results apply to hybrid solid state systems and can turn out to be helpful to find the most appropriate description of leakage in the recent developments of cavity quantum electrodynamics.

We analyze a local approach to the non-Markovian evolution of open quantum systems. It turns out that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. The price one pays for the local approach is that the corresponding generator might be highly singular and it keeps the memory about the starting point "t₀". This is the very essence of non-Markovianity. We illustrate a local approach by simple examples.

We construct a non-Markovian dynamical map that accounts for systems correlated to the environment. We refer to it as a canonical dynamical map, which forms an evolution family. The relationship between inverse maps and correlations with the environment is established. The mathematical properties of complete positivity is related to classical correlations, according to quantum discord, between the system and the environment. A generalized non-Markovian master equation is derived from the canonical dynamical map.

We review some notions for quantum dynamical entropies. The dynamical entropy of quantum systems is discussed and a numerical computation of the dynamical entropy is carried for the open system dynamics.

We study general properties of dynamical maps preserving Hermiticity and quasi-Hermiticity, and prove that the generator of a dynamical semigroup is always a pseudo-Hermitian operator. Moreover, improving a previous proposal by Jakob and Stenholm, we introduce two new Lyapunov functionals for degenerate open systems, and apply such results to a physical example.

We describe the evolution of the quantum entanglement in a system composed of two interacting bosonic modes immersed in a thermal reservoir, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. The evolution of entanglement is described in terms of the covariance matrix for Gaussian initial states. We calculate the logarithmic negativity and show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and the strength of interaction between the two modes. After its generation one can observe temporary suppressions and revivals of the entanglement. For entangled initial squeezed thermal states, entanglement suppression takes place, for all temperatures of the reservoir, and temporary revivals and suppressions of entanglement can be observed too. In the limit of infinite time the system evolves asymptotically to an equilibrium state which may be entangled or separable.