Dynamics Of Open Systems Research Articles

Dissipation production in a closed two-level quantum system as a test of the irreversibility of the dynamics.

Irreversible behavior in open stochastic dynamical systems is quantified by stochastic entropy production, a property that measures the difference in likelihoods of forward and subsequent backward system evolution. But for a closed system, governed by deterministic dynamics, such an approach is not appropriate. Instead, we can consider the difference in likelihoods of forward and "obverse" behavior: the latter being a backward trajectory initiated at the same time as the forward trajectory. Such a comparison allows us to define "dissipation production," an analog of stochastic entropy production. It quantifies the breakage of a property of the evolution termed "obversibility" just as stochastic entropy production quantifies a breakage of reversibility. Both are manifestations of irreversibility. In this study we discuss dissipation production in a quantum system. We consider a simple, deterministic, two-level quantum system characterized by a statistical ensemble of state vectors, and we provide numerical results to illustrate the ideas. We consider cases that both do and do not satisfy an Evans-Searles Fluctuation Theorem for the dissipation production, and hence identify conditions under which the system displays time-asymmetric average behavior: an arrow of time.

АКТУАЛЬНЫЕ ПРОБЛЕМЫ ПРЕПОДАВАНИЯ ПРАВА В СОВРЕМЕННОЙ ШКОЛЕ

This article discusses the current problems of teaching law in a modern school, conditionally divided by the author into two main groups. In addition the author directly takes into account the specifics of law as a dynamic open system, which is characterized by constant changes - the peculiarities of teaching law should be reduced to reporting on the specifics of the law to students. The author not only identifies the main problems in the field of teaching law, but also identifies possible ways to solve them.

Time-Linear Quantum Transport Simulations with Correlated Nonequilibrium Green’s Functions

We present a time-linear scaling method to simulate open and correlated quantum systems out of equilibrium. The method inherits from many-body perturbation theory the possibility to choose selectively the most relevant scattering processes in the dynamics, thereby paving the way to the real-time characterization of correlated ultrafast phenomena in quantum transport. The open system dynamics is described in terms of an ``embedding correlator'' from which the time-dependent current can be calculated using the Meir-Wingreen formula. We show how to efficiently implement our approach through a simple grafting into recently proposed time-linear Green's function methods for closed systems. Electron-electron and electron-phonon interactions can be treated on equal footing while preserving all fundamental conservation laws.

Thermodynamic model of MSWI flue gas cooling path: Effect of flue gas composition on heavy metal binding forms.

In the context of circular economy and heavy metal (HM) recovery from municipal solid waste incineration (MSWI) fly ash (FA), detailed knowledge of HM binding forms is required for achieving higher extraction rates. The FA mineralogy is still poorly understood due to its low grain size and low metal concentration. To investigate the HM binding forms, a sophisticated thermodynamic reactive transport model was developed to simulate ash-forming processes. The stability of different binding forms was investigated at different flue gas conditions (varying ratios of HCl, SO2, O2) by simulating the gas cooling path in closed system and dynamic open system, where the gas composition is changing upon cooling due to precipitation of solids. The simulations predict that at flue gas conditions of molar ratio S/Cl < 1, Cu and Zn precipitate as oxides (and Zn silicates) at approximately 650°C. At temperatures <300°C, Zn, Cu, Pb and Cd are predicted to precipitate as easily soluble chlorides. In flue gas with molar ratio S/Cl > 1, the HM precipitate as less soluble sulphates. The results indicate that the less soluble HM fraction in the electrostatic precipitator ash represent oxides and silicates that formed in the boiler section but were transported to the electrostatic precipitator. The model provides insight into the physical-chemical processes controlling the metal accumulation in the flue gas and FA during the cooling of the flue gas. The obtained data serve as valuable basis for improving metal recovery from MSWI FA.

Convex Optimization for Nonequilibrium Steady States on a Hybrid Quantum Processor.

Finding the transient and steady state properties of open quantum systems is a central problem in various fields of quantum technologies. Here, we present a quantum-assisted algorithm to determine the steady states of open system dynamics. By reformulating the problem of finding the fixed point of Lindblad dynamics as a feasibility semidefinite program, we bypass several well-known issues with variational quantum approaches to solving for steady states. We demonstrate that our hybrid approach allows us to estimate the steady states of higher dimensional open quantum systems and discuss how our method can find multiple steady states for systems with symmetries.

Higher-order mean-field theory of chiral waveguide QED

Waveguide QED with cold atoms provides a potent platform for the study of non-equilibrium, many-body, and open-system quantum dynamics. Even with weak coupling and strong photon loss, the collective enhancement of light-atom interactions leads to strong correlations of photons arising in transmission, as shown in recent experiments. Here we apply an improved mean-field theory based on higher-order cumulant expansions to describe the experimentally relevant, but theoretically elusive, regime of weak coupling and strong driving of large ensembles. We determine the transmitted power, squeezing spectra and the degree of second-order coherence, and systematically check the convergence of the results by comparing expansions that truncate cumulants of few-particle correlations at increasing order. This reveals the important role of many-body and long-range correlations between atoms in steady state. Our approach allows to quantify the trade-off between anti-bunching and output power in previously inaccessible parameter regimes. Calculated squeezing spectra show good agreement with measured data, as we present here.

Opportunities for system dynamics research in operations management for public policy

Operations management (OM) in the public policy context is extremely complex with many mutually interacting factors characterized by feedback loops, delays and nonlinearities, as well as multiple stakeholders pursuing divergent objectives. Prior researchers have called for a systems approach in these contexts, arguing that standard OM methodologies such as mathematical programming, and queuing theory often cannot fully address these problems. Researchers have employed one such systems approach, system dynamics, successfully for decades for studying OM problems in public policy because it can address such complexity and can also integrate disciplines from outside OM such as political science, epidemiology, ecology, etc. In this paper, we create a roadmap for researchers—both those who are familiar with systems dynamics and those who are not—for the expanded use of system dynamics studying public policy‐related OM problems. We review and organize relevant system dynamics literature in both traditional operations management venues as well as public policy venues unfamiliar to OM audiences. We then identify a set of interesting open questions and potential system dynamics building blocks for answering them by topic. Leveraging this review, we describe under what conditions system dynamics is most appropriate. We then identify several overarching methodological and domain gaps for future research. Finally, we build on previous work to extend a process for using system dynamics with traditional operations management methodologies. It separates model building into two sequential phases: consensus‐building models and detailed operational models. It also incorporates scenario planning and feedback from implementation outcomes.

Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation.

Dissipaton theory had been proposed as an exact, nonperturbative approach to deal with open quantum system dynamics, where the influence of the Gaussian environment is characterized by statistical quasi-particles, named dissipatons. In this work, we revisit the dissipaton equation of motion theory and establish an equivalent dissipaton-embedded quantum master equation (DQME) that gives rise to dissipatons as generalized Brownian particles. As explained in this work, the DQME supplies a direct approach to investigate the statistical characteristics of dissipatons and, thus, the physically supporting hybrid bath modes. Numerical demonstrations are carried out on the electron transfer model, exhibiting the transient statistical properties of the solvation coordinate.

Tree tensor network state approach for solving hierarchical equations of motion.

The hierarchical equations of motion (HEOM) method is a numerically exact open quantum system dynamics approach. The method is rooted in an exponential expansion of the bath correlation function, which in essence strategically reshapes a continuous environment into a set of effective bath modes that allow for more efficient cutoff at finite temperatures. Based on this understanding, one can map the HEOM method into a Schrödinger-like equation, with a non-Hermitian super-Hamiltonian for an extended wave function being the tensor product of the central system wave function and the Fock state of these effective bath modes. In this work, we explore the possibility of representing the extended wave function as a tree tensor network state (TTNS) and the super-Hamiltonian as a tree tensor network operator of the same structure as the TTNS, as well as the application of a time propagation algorithm using the time-dependent variational principle. Our benchmark calculations based on the spin-boson model with a slow-relaxing bath show that the proposed HEOM+TTNS approach yields consistent results with those of the conventional HEOM method, while the computation is considerably sped up. In addition, the simulation with a genuine TTNS is four times faster than a one-dimensional matrix product state decomposition scheme.

Optimality and Complexity in Measured Quantum-State Stochastic Processes

If an experimentalist observes a sequence of emitted quantum states via either projective or positive-operator-valued measurements, the outcomes form a time series. Individual time series are realizations of a stochastic process over the measurements’ classical outcomes. We recently showed that, in general, the resulting stochastic process is highly complex in two specific senses: (i) it is inherently unpredictable to varying degrees that depend on measurement choice and (ii) optimal prediction requires using an infinite number of temporal features. Here, we identify the mechanism underlying this complicatedness as generator nonunifilarity—the degeneracy between sequences of generator states and sequences of measurement outcomes. This makes it possible to quantitatively explore the influence that measurement choice has on a quantum process’ degrees of randomness and structural complexity using recently introduced methods from ergodic theory. Progress in this, though, requires quantitative measures of structure and memory in observed time series. And, success requires accurate and efficient estimation algorithms that overcome the requirement to explicitly represent an infinite set of predictive features. We provide these metrics and associated algorithms, using them to design informationally-optimal measurements of open quantum dynamical systems.

Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations.

We present a quantum algorithm based on the generalized quantum master equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system-bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining degrees of freedom is used as input to calculate the corresponding non-unitary propagator. We demonstrate how the Sz.-Nagy dilation theorem can be employed to transform the non-unitary propagator into a unitary one in a higher-dimensional Hilbert space, which can then be implemented on quantum circuits of NISQ computers. We validate our quantum algorithm as applied to the spin-boson benchmark model by analyzing the impact of the quantum circuit depth on the accuracy of the results when the subset is limited to the diagonal elements of the reduced density matrix. Our findings demonstrate that our approach yields reliable results on NISQ IBM computers.

QuantumDynamics.jl: A modular approach to simulations of dynamics of open quantum systems.

A simulation of the non-adiabatic dynamics of a quantum system coupled to dissipative environments poses significant challenges. New sophisticated methods are regularly being developed with an eye toward moving to larger systems and more complicated descriptions of solvents. Many of these methods, however, are quite difficult to implement and debug. Furthermore, trying to make the individual algorithms work together through a modular application programming interface can be quite difficult as well. We present a new, open-source software framework, QuantumDynamics.jl, designed to address these challenges. It provides implementations of a variety of perturbative and non-perturbative methods for simulating the dynamics of these systems. Most prominently, QuantumDynamics.jl supports hierarchical equations of motion and methods based on path integrals. An effort has been made to ensure maximum compatibility of the interface between the various methods. Additionally, QuantumDynamics.jl, being built on a high-level programming language, brings a host of modern features to explorations of systems, such as the usage of Jupyter notebooks and high level plotting, the possibility of leveraging high-performance machine learning libraries for further development. Thus, while the built-in methods can be used as end-points in themselves, the package provides an integrated platform for experimentation, exploration, and method development.

Wigner-molecularization-enabled dynamic nuclear polarization

Multielectron semiconductor quantum dots (QDs) provide a novel platform to study the Coulomb interaction-driven, spatially localized electron states of Wigner molecules (WMs). Although Wigner-molecularization has been confirmed by real-space imaging and coherent spectroscopy, the open system dynamics of the strongly correlated states with the environment are not yet well understood. Here, we demonstrate efficient control of spin transfer between an artificial three-electron WM and the nuclear environment in a GaAs double QD. A Landau–Zener sweep-based polarization sequence and low-lying anticrossings of spin multiplet states enabled by Wigner-molecularization are utilized. Combined with coherent control of spin states, we achieve control of magnitude, polarity, and site dependence of the nuclear field. We demonstrate that the same level of control cannot be achieved in the non-interacting regime. Thus, we confirm the spin structure of a WM, paving the way for active control of correlated electron states for application in mesoscopic environment engineering.

Full counting statistics and coherences: Fluctuation symmetry in heat transport with the unified quantum master equation.

Recently, a "unified" quantum master equationwas derived and shown to be of the Gorini-Kossakowski-Lindblad-Sudarshan form. This equationdescribes the dynamics of open quantum systems in a manner that forgoes the full secular approximation and retains the impact of coherences between eigenstates close in energy. We implement full counting statistics with the unified quantum master equationto investigate the statistics of energy currents through open quantum systems with nearly degenerate levels. We show that, in general, this equationgives rise to dynamics that satisfy fluctuation symmetry, a sufficient condition for the Second Law of Thermodynamics at the level of average fluxes. For systems with nearly degenerate energy levels, such that coherences build up, the unified equation is simultaneously thermodynamically consistent and more accurate than the fully secular master equation. We exemplify our results for a "V" system facilitating energy transport between two thermal baths at different temperatures. We compare the statistics of steady-state heat currents through this system as predicted by the unified equationto those given by the Redfield equation, which is less approximate but, in general, not thermodynamically consistent. We also compare results to the secular equation, where coherences are entirely abandoned. We find that maintaining coherences between nearly degenerate levels is essential to properly capture the current and its cumulants. On the other hand, the relative fluctuations of the heat current, which embody the thermodynamic uncertainty relation, display inconsequential dependence on quantum coherences.

Symmetry classes of dissipative topological insulators with edge dark states

We classify the dissipative topological insulators (TIs) with edge dark states (EDSs) by using the 38-fold way of non-Hermitian systems in this paper. The dissipative dynamics of these quadratic open fermionic systems is captured by a non-Hermitian single-particle matrix which contains both the internal dynamics and the dissipation, referred to as the damping matrix $X$. The dark states in these systems are the eigenmodes of $X$ in which the eigenvalues' imaginary part vanishes. However, there is a constraint on $X$, namely, that the modes in which the eigenvalues' imaginary parts are positive are forbidden. In other words, the imaginary line-gap of $X$ is ill-defined, so the topological band theory classifying the dark states cannot be applied to $X$. To reveal the topological protection of the EDSs, we propose the double damping matrix $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{X}=\text{diag}(X,{X}^{*})$, where the imaginary line-gap is well-defined. Thus, the 38-fold way can be applied to $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{X}$, and the topological protection of the EDS is uncovered. Different from previous studies of EDSs in purely dissipative dynamics, the EDSs in the dissipative TIs are robust against the inclusion of Hamiltonians. Furthermore, the topological classification of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{X}$ not only reflects the topological protection of EDSs in dissipative TIs but also provides a paradigm to predict the appearance of EDSs in other open free fermionic systems.

Dynamic stability of slightly curved tensioned pipe conveying pressurized hot two phase fluid resting on non uniform foundation

The dynamic stability of slightly curved tensioned pipes conveying pressurized two phase fluid, under thermal loadings are investigated in this paper. Furthermore, these pipes are resting on nonuniform elastic foundations. The equation of motion of the system is derived using the extended Hamilton’s principle for open dynamic systems and considering the Euler–Bernoulli theory for slender beams. The free vibration and the effects of two phase fluid flow, geometric imperfections, thermal, tension and pressure on the pipe system resting on nonuniform foundations are investigated numerically. Three different boundary conditions (BC) are considered, namely simply-simply (SS) supported, simply-clamped (SC) supported and clamped-clamped (CC) supported. The numerical method of Finite Element was used on the partial differential equation. This method is used to accurately predict steady state natural frequency responses of a dynamical system through several numerical investigations. It was found that the stability of slightly curved pipes conveying two phase flow are significantly affected by the boundary condition. It is shown that the initial curvature term increases the critical velocities for all the nine modes considered, the increase is significant in the first and second critical velocities compared to the other modes. Initial curvature effect is more pronounced in simple supported ends. Further-more the influence of the fluid velocity, temperature, pressure and axial tension is analysed; the results show that the vibration frequency decreases when the fluid velocity, temperature, and pressure increase or the axial tension decreases, and the critical fluid velocity decreases when the temperature and pressure increase or the axial tension decreases. For the pipe on nonuniform foundation, an increased stiffness leads to an increased in the first critical velocity for all the BC. However, the pattern of the increment depends on the attachment parameter, initial curvature, and the vapour quality. Some of these results are completely absent in pipes conveying single flows.

Introduction to the theory of open quantum systems

This manuscript is an edited and refined version of the lecture script for a one-semester graduate course given originally at the PhD school in the Institute of Physics of Polish Academy of Sciences in the Spring/Summer semester of 2022. The course expects from the student only a basic knowledge on graduate-level quantum mechanics. The script itself is largely self-contained and could be used as a textbook on the topic of open quantum systems. The program of this course is based on a novel approach to the description of the open system dynamics: It is showed how the environmental degrees of freedom coupled to the system can be represented by a multi-component quasi-stochastic process. Using this representation one constructs the super-quasi-cumulant (or super-qumulant) expansion for the system’s dynamical map-a parametrization that naturally lends itself for the development of a robust and practical perturbation theory. Thus, even an experienced researcher might find this manuscript of some interest.

Quantum circuit simulation of superchannels

Quantum simulation is one of the central discipline to demonstrate the power of quantum computing. In recent years, the theoretical framework of quantum superchannels has been developed and applied widely as the extension of quantum channels. In this work, we study the quantum circuit simulation task of superchannels. We develop a quantum superchannel simulation algorithm based on the convex decomposition into sum of extreme superchannels. We demonstrate the algorithm by numerical simulation of qubit superchannels with high accuracy, making it applicable to current experimental platforms. Our study stands as an expansion of the superchannel theory to the field of quantum simulation and algorithm, as well as an extension of quantum simulation from channels and open-system dynamics to superchannels and processes with manifest quantum memory effects.

Quantum non-Markovianity: Overview and recent developments

In the current era of noisy intermediate-scale quantum (NISQ) devices, research on the theory of open system dynamics has a crucial role to play. In particular, understanding and quantifying memory effects in quantum systems is critical to gain a better handle on the effects of noise in quantum devices. The main focus of this review is to address the fundamental question of defining and characterizing such memory effects—broadly referred to as quantum non-Markovianity—utilizing various approaches. We first discuss the two-time-parameter maps approach to open system dynamics and review the various notions of quantum non-Markovianity that arise in this paradigm. We then discuss an alternate approach to quantum stochastic processes based on the quantum combs framework, which accounts for multi-time correlations. We discuss the interconnections and differences between these two paradigms and conclude with a discussion on the necessary and sufficient conditions for quantum non-Markovianity.

Interplay between Non-Markovianity of Noise and Dynamics in Quantum Systems.

The non-Markovianity of open quantum system dynamics is often associated with the bidirectional interchange of information between the system and its environment, and it is thought to be a resource for various quantum information tasks. We have investigated the non-Markovianity of the dynamics of a two-state system driven by continuous time random walk-type noise, which can be Markovian or non-Markovian depending on its residence time distribution parameters. Exact analytical expressions for the distinguishability as well as the trace distance and entropy-based non-Markovianity measures are obtained and used to investigate the interplay between the non-Markovianity of the noise and that of dynamics. Our results show that, in many cases, the dynamics are also non-Markovian when the noise is non-Markovian. However, it is possible for Markovian noise to cause non-Markovian dynamics and for non-Markovian noise to cause Markovian dynamics but only for certain parameter values.