Dynamics Of Open Systems Research Articles

Dynamics of a driven open double two-level system and its entanglement generation

We investigate the dynamics of the driven open double two-level system by deriving a driven Markovian master equation based on the Lewis-Riesenfeld invariant theory. The transitions induced by coupling to the heat reservoir occur between the instantaneous eigenstates of the Lewis-Riesenfeld invariant. Therefore, different driving protocols associated with corresponding Lewis-Riesenfeld invariants result in different open system dynamics and symmetries. In particular, we show that since the instantaneous steady state of the driven double two-level system is one of eigenstates of the Lewis-Riesenfeld invariant at ultralow reservoir temperature, the inverse engineering method based on the Lewis-Riesenfeld invariants has a good performance in rapidly preparing the quantum state of open quantum systems. As an example, a perfect entangled state is generated by means of the inverse engineering method.

DIGITALIZATION IN UNIVERSITY EDUCATION: DIDACTIC ASPECTS

Intensively developing digital technologies are transforming the basic processes studied by the didactics of higher education: ways of the teacher-student interrelated activity; the student and the knowledge, skills, and competencies intended to be learnt and gained; the teacher and the methodology of educational material. The learning goals set by the information society shift the focus from mastering the system of knowledge and developing professional skills to developing competencies, the formation of students’ readiness to design their own unique educational trajectories based on a competency-based approach. As higher education becomes more digitalized, there is a shift from coordinating teaching and learning activities to projecting, forming, and mastering individual educational plans. To meet the challenges of modern education, educators are expected to be able to comprehend changes impacting all of the components of didactic theory, including goals, content, forms, technologies, and learning tools. Digitalization processes lead to the dominance of infographic forms of presentation of educational material instead of narrative (text) forms associated with the development of voluminous texts. The variety of forms of organization of educational activities in the digital educational environment is increasing significantly, they are becoming a dynamic open system of educational modules. The educators are being faced with new theoretical tasks due to the active modernization of university educational practice, including the need to find ways to implement continuity between traditional and innovative methods of organizing the educational process while taking into account specific cognitive, motivational, and need-based characteristics of the digital generation. The transition from teaching as the educators’ primary activity to the variety of pedagogical roles they play in the digital educational process actualizes teachers’ mastery of the information technologies and the development of their personal professional teaching strategy.

Towards the Resolution of a Quantized Chaotic Phase-Space: The Interplay of Dynamics with Noise.

We outline formal and physical similarities between the quantum dynamics of open systems and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, which, for suitable timescales, becomes analogous to the Fokker-Planck equation describing classical advection and diffusion. This correspondence allows, in principle, to surmise a finite resolution, other than the Planck scale, for the quantized state space of the open system, particularly meaningful when the latter underlies chaotic classical dynamics. We provide representative examples of the quantum-stochastic parallel with noisy Hopf cycles and Van der Pol-type oscillators.

Pre-eruptive dynamics at the Campi Flegrei Caldera: from evidence of magma mixing to timescales estimates

We review pre-eruptive dynamics and evidence of open-system behavior in the volcanic plumbing system beneath Campi Flegrei Caldera, together with estimates of magma residence time, magma ascent, and mixing-to-eruption timescales. In detail, we compile pre- and syn-eruptive dynamics reported in the literature for (a) the Campanian Ignimbrite ~ 40 ka, (b) the Neapolitan Yellow Tuff (~ 15 ka), and (c) the recent activity within the Phlegrean area. We first summarize geochemical and textural evidence (e.g., magma mixing, crystal disequilibria, vertical zonings, and isotopic records) of open-system behavior for the pyroclasts erupted in the last 40 ky at Campi Flegrei Caldera. We show that the fingerprint of open-system dynamics is ubiquitous in the deposits associated with the volcanic activity at the Campi Flegrei Caldera in the last 40 ky. Then, we describe the results of geophysical and petrological investigations that allow us to hypothesize the structure of the magma feeding system. We point to a trans-crustal magmatic feeding system characterized by a main storage reservoir hosted at ~ 9 km that feeds and interacts with shallow reservoirs, mainly placed at 2–4 km. Finally, we define a scenario depicting pre-eruptive dynamics of a possible future eruption and provide new constraints on timescales of magma ascent with a physical model based on magma-driven ascending dyke theory. Results show that considerably fast ascent velocities (i.e., of the order of m/s) can be easily achieved for eruptions fed by both shallow (i.e., 3–4 km) and deep (i.e., ~ 9 km) reservoirs. Comparing the results from experimental and numerical methods, it emerges that mixing-to-eruption timescales occurring at shallow reservoirs could be on the order of minutes to hours. Finally, we highlight the volcanological implications of our timescale estimates for magma ascent and mixing to eruption. In particular, explosive eruptions could begin with little physical ‘warning’, of the order of days to months. In this case, the onset of volatile saturation might provide pre-eruptive indicators.Graphical

Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems

Non-Markovian open quantum systems represent the most general dynamics when the quantum system is coupled with a bath environment. The quantum dynamics arising from many important applications are non-Markovian. Although for special cases, such as Hamiltonian evolution and Lindblad evolution, quantum simulation algorithms have been extensively studied, efficient quantum simulations for the dynamics of non-Markovian open quantum systems remain underexplored. The most immediate obstacle for studying such systems is the lack of a universal succinct description of their dynamics. In this work, we fulfill the gap of studying such dynamics by (1) providing a succinct representation of the dynamics of non-Markovian open quantum systems with quantifiable error, and (2) developing an efficient quantum algorithm for simulating such dynamics with cost $${\mathcal {O}}(t\, \textrm{polylog}(t/\epsilon ))$$ for evolution time t and precision $$\epsilon $$ . Our derivation of the succinct representation is based on stochastic Schrödinger equations, which could lead to new alternatives to deal with open quantum systems as well.

Dynamics of closed quantum systems under stochastic resetting

We consider a closed quantum system subject to a stochastic resetting process. The generic expression for the resulting density operator is formulated for arbitrary resetting dynamics, fully characterised by the distribution of times between consecutive reset events. We analyse the behaviour of the state in the long-time regime, as well as the evolution of relevant quantities in the study of quantum coherence and closed- versus open-system dynamics. Our general results are complemented with examples involving particular resetting distributions, and special attention is paid to the two-level (qubit) system, in which we elucidate the effects of the renewal process on the speed of evolution toward an orthogonal state, and gain insight into the resetting applied to open systems.

On optimization of coherent and incoherent controls for two-level quantum systems

This paper considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schrödinger equation with coherent control. The open system dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation whose Hamiltonian depends on coherent control and superoperator of dissipation depends on incoherent control. For the closed system, we consider the problem of generation of the phase shift gate for some values of phases and final times for which we numerically show that zero coherent control, which is a stationary point of the objective functional, is not optimal; it gives an example of subtle point for practical solving quantum control problems. The two-stage method, which was developed in [48] for generic $N$-level open quantum systems for approximate generation of a given target density matrix, is modified here for the case of two-level systems. We modify the first ("incoherent") stage by numerically optimizing piecewise constant incoherent control instead of using constant incoherent control analytically computed using eigenvalues of the target density matrix. Exact analytical formulas are derived for the system state evolution, the objective functions and their gradients for the modified first stage. These formulas are then applied in the two-step gradient projection method. The numerical simulations show that the modified first stage duration can be significantly less than the unmodified first stage duration, but at the cost of performing optimization in the class of piecewise constant controls.

On optimization of coherent and incoherent controls for two-level quantum systems

This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schrödinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation whose Hamiltonian depends on coherent control and superoperator of dissipation depends on incoherent control. For the closed system, we consider the problem for generation of the phase shift gate for some values of phases and final times for which we numerically show that zero coherent control, which is a stationary point of the objective functional, is not optimal; it gives an example of subtle point for practical solving quantum control problems. The two-stage method, which was developed in [A. Pechen, Phys. Rev. A., 84, 042106 (2011)] for generic $N$-level open quantum systems for approximate generation of a given target density matrix, is modified here for the case of two-level systems. We modify the first ("incoherent") stage by numerically optimizing piecewise constant incoherent control instead of using constant incoherent control analytically computed using eigenvalues of the target density matrix. Exact analytical formulas are derived for the system's state evolution, the objective functions and their gradients for the modified first stage. These formulas are then applied in the two-step gradient projection method. The numerical simulations show that the modified first stage's duration can be significantly less than the unmodified first stage's duration, but at the cost of performing optimization in the class of piecewise constant controls. Bibliography: 72 titles.

Two types of neural network representations of quantum mixed states

Quantum information and artificial intelligence are the two most cutting-edge research fields in recent years, which have made a lot of progress in changing the traditional science. It has become a hot topic of research to realize the cross fusion of the two fields. Scholars have made many explorations in this field. For example, they have simulated the steady state and the dynamics of open quantum many-body systems. However, little attention has been paid to the problem of accurate representation of neural networks. In this paper, we focus on neural network representations of quantum mixed states. We first propose neural network quantum mixed virtual states (NNQMVS) and neural network quantum mixed states (NNQMS) with general input observables by using two neural network architectures, respectively. Then we explore their properties and obtain the related conclusions of NNQMVS and NNQMS under tensor product operation and local unitary operation.To quantify the approximation degree of normalized NNQMVS and NNQMS for a given mixed state, we define the best approximation degree by using normalized NNQMVS and NNQMS, and obtain the necessary and sufficient conditions for the representability of a general mixed state by using normalized NNQMVS and NNQMS. Moreover, we explore the types of mixed states that can be represented by these two neural network architectures and show their accurate neural network representations.

ПРОБЛЕМЫ ЦИФРОВОЙ ТРАНСФОРМАЦИИ СУБЪЕКТОВ РОССИЙСКОЙ ФЕДЕРАЦИИ

The work is devoted to the study of the processes of digital transformation of economic entities considered as open socio-economic systems. With the use of statistical data, the further development of digital transformation processes, as well as the need to develop information-analytical and methodological support for the management of these processes, is substantiated. The essence is systematized and the author's concept of digital transformation of the socio-economic system is developed, its goals and directions for various levels of the economy are considered. The stages, directions and indicators of the digital transformation of public administration are considered. The directions and dynamics of the digital transformation of the subjects of the Russian Federation and its problems are studied. The purpose of the study is to study digital transformation in the context of managing the development of socio-economic systems, states of the subject, object and management system, as well as the formation of a complex of problem fields of digital transformation of the subjects of the Russian Federation in the context of their functional, structural, resource and information characteristics as open dynamic socio-economic systems. Materials and methods. The statistical basis of the new study was data from Russian and foreign analytical agencies, data from Rosstat and international statistical databases that characterize the processes of informatization and digitalization of the Russian and world economies, data on digital transformation strategies of the constituent entities of the Russian Federation, presented on the websites of the Government of Russia, federal and regional executive authorities. The study used methods of correlation-regression, cluster, structural and content analysis, as well as a systematic approach. The theoretical and methodological base was the work of Russian and foreign researchers, reports of world and Russian consulting agencies and research centers, legal documents of the Russian Federation and international organizations. Results. The role, meaning and functions of digitalization are systematized. A definition of digital transformation has been developed as a characteristic of a socio-economic system used to describe the goals, process and results of digital deve¬lopment, leading to a transformational change in the parameters of the control and managed systems, transferring systems to a qualitatively new level, which manifests itself in a radical change in the business model, business processes, products and services. Regional disproportions in the digital development of the constituent entities of the Russian Federation are diagnosed. The problematic fields of digital transformation of the subjects of the Russian Federation are identified in the context of 4 components – their functional, structural, informational and resource description as SES. Conclusion. The developed concept of digital transformation is based on the system paradigm and can be used to develop a set of methods, models, indicators and indicators for the digital development of socio-economic systems. The developed complex of problematic fields of digital transformation of the subjects of the Russian Federation as SES can be used to develop management decision support systems, activate the digital development of the subjects of the Russian Federation, increase its effectiveness, efficiency and sustainability.

Неолексеми з компонентом медіа у словниках і науковому дискурсі із соціальних комунікацій

The article analyzes the array of innovative lexis which includes the component media and comprises 425 units from the perspective of mediadeterminism. The lexemes have been chosen using the Ukrainian lexicographic sources, the academic papers in the field of social communications and medialinguistics and also the monitoring of the Ukrainian Internet sector conducted during the period of January-March, 2023. The neolexemes with the component media have been proven to be an open dynamic system replenished constantly under the influence of technologies and socio-communicative transformations. This was confirmed by the monitoring of their description in the Ukrainian etymological and specialized dictionaries starting from 1973. The dynamics of the entry of neologisms as the terms into the academic discourse is traced on the example of two numbers of special publications on social communications for 2010 and 2022. The study has revealed the increase in frequency of using the terms with the component media, the heterogeneity of their fixation as neographisms, the living process of synonymization of the lexemes mass media and media, as well as the tendency for autochthonization of the indeclinable word form media. The paper shows the way for the further systemizing of the collected array of lexical units and its representation as a qualitative-quantitative hierarchic structure that contains the nominations of media space with its technical, technological, and socio-communicative components as the reference points. The most verbalized areas of the media space can serve as the indicators of media social spheres. The accumulated database of neolexemes with the component media can prove to be useful for lexicographic purposes.

On the role of initial coherence in the spin phase-space entropy production rate

Recent studies have pointed out the intrinsic dependence of figures of merit of thermodynamic relevance—such as work, heat and entropy production—on the amount of quantum coherences that is made available to a system. However, whether coherences hinder or enhance the value taken by such quantifiers of thermodynamic performance is yet to be ascertained. We show that, when considering entropy production generated in a process taking a finite-size bipartite quantum system out of equilibrium through local non-unitary channels, no general monotonicity relationship exists between the entropy production and degree of quantum coherence in the state of the system. A direct correspondence between such quantities can be retrieved when considering specific forms of open-system dynamics applied to suitably chosen initial states. Our results call for a systematic study of the role of genuine quantum features in the non-equilibrium thermodynamics of quantum processes.

Keeping the Spirit in the Bottle: On Pathological Reduction of Information in Totalitarianism

This article begins with disputing the teleologically charged notion of unstoppable information growth, pointing at the alternation of informational contraction and expansion in open dynamic systems. Narrowing the focus, it turns to the 20th century totalitarian systems as particularly paradoxical informational environments: Being less capable of processing information than their democratic counterparts and therefore more vulnerable to overloads, they are particularly prone to suppressing informational transmission in some areas, codes and media. Dilution and conflation are singled out as the most common ways of lessening the informational value of communication in totalitarian societies. Whereas the first greatly increases the ratios of signs to messages and messages to interactions, causing redundancy and semantic inflation, the second rolls back preexisting functional differentiations (person vs. social role, sender vs. message, message vs. information etc.) within societies and their communicative system. It is argued that both attempts at semantic impoverishment of public communication in totalitarianism lead to the pathological states, failing to reduce the overall amount of information within the systems in question and precipitating the very informational explosions they were designed to prevent.

TOOLKIT FOR ENSURING SYSTEMIC DEVELOPMENT OF HEALTH CARE INSTITUTIONS IN UKRAINE

The research emphasizes the objectively existing need, as well as the problem of ensuring effective management of the systemic development of health care institutions in Ukraine, in particular in the segment of private ownership. The purpose of the study is to determine the scientific substantiation of the theoretical, methodological and applied characteristics of the implementation of the toolkit for ensuring the systemic development of health care institutions in Ukraine, which provides for institutional and structural reforms in the field for the sake of organizations and the constant improvement of the quality of medical care for the population in accordance with international standards. It is shown that every enterprise is an open complex dynamic system that functions in a defined external environment. The modern socio-economic environment is characterized by a high rate of change, which can sometimes be predicted with low probability. Maintaining the existing state of the enterprise and moving forward is possible only under conditions of effective adaptation of the enterprise to changes in the external environment Options for ensuring systemic development of health care institutions, namely, internal growth due to more effective use of own resource potential; redistribution of internal resources, focusing them on progressive types of economic activity; termination of the provision of a number of services that require higher quality resources, in their real absence; transfer of certain types of activities, not provided with resources, to other performers on a contractual basis; merger / acquisition with the aim of improving the system of medical care of the population. The advantages and disadvantages and peculiarities of practical implementation of relevant strategic decisions are indicated. The scientific novelty of the research results lies in the further development of methodological and applied principles of strategic management of the development of health care institutions due to the identification of strategic alternatives for the efficiency of activities, as well as tools and means, the implementation of which ensures systemic development. The applied value of the research results lies in the development of various scenarios for the further balanced development of health care institutions.

Non-Markovian Abraham-Lorentz-Dirac equation: Radiation reaction without pathology

Motion of a point charge emitting radiation in an electromagnetic field obeys the Abraham-Lorenz-Dirac (ALD) equation, with the effects of radiation reaction or self-force incorporated. This class of equations describing backreaction, including also the equations for gravitational self-force or Einstein's equation for cosmology driven by trace anomaly, contain third-order derivative terms. They are known to have pathologies like the possession of runaway solutions, causality violation in pre-acceleration and the need for an extra second-order derivative initial condition. In our current program we reexamine this old problem from the perspective of non-Markovian dynamics in open systems, applied earlier to backreaction problems in the early universe. Here we consider a harmonic atom coupled to a scalar field, which acts effectively like a supra-Ohmic environment, as in scalar electrodynamics. Our analysis shows that a) there is no need for specifying a second derivative for the initial condition; b) there is no pre-acceleration. These undesirable features in conventional treatments arise from an inconsistent Markovian assumption: these equations were regarded as Markovian ab initio, not as a limit of the backreaction-imbued non-Markovian equation of motion. If one starts with the full non-Markovian dynamical equation and takes the proper Markovian limit judiciously, no harms are done. Finally, c) There is no causal relation between the higher-derivative term in the equation of motion and the existence of runaway solutions. If the charge has an effective size greater than this critical value, its dynamics is stable. When this reasonable condition is met, radiation reaction understood and treated correctly in the non-Ohmic non-Markovian dynamics still obeys a third-order derivative equation, but it does not require a second derivative initial condition, and there is no pre-acceleration.

Dynamics of open quantum nuclear systems: the case of 8B breakup

Dynamics of open quantum nuclear systems: the case of 8B breakup

Wave Function Realization of a Thermal Collision Model.

An efficient algorithm to simulate dynamics of open quantum system is presented. The method describes the dynamics by unraveling stochastic wave functions converging to a density operator description. The stochastic techniques are based on the quantum collision model. Modeling systems dynamics with wave functions and modeling the interaction with the environment with a collision sequence reduces the scale of the complexity significantly. The algorithm developed can be implemented on quantum computers. We introduce stochastic methods that exploit statistical characteristics of the model such as Markovianity, Brownian motion, and binary distribution. The central limit theorem is employed to study the convergence of distributions of stochastic dynamics of pure quantum states represented by wave vectors. By averaging a sample of functions in the distribution we prove and demonstrate the convergence of the dynamics to the mixed quantum state described by a density operator.

Information theoretical limits for quantum optimal control solutions: error scaling of noisy control channels.

Accurate manipulations of an open quantum system require a deep knowledge of its controllability properties and the information content of the implemented control fields. By using tools of information and quantum optimal control theory, we provide analytical bounds (information-time bounds) to characterize our capability to control the system when subject to arbitrary sources of noise. Moreover, since the presence of an external noise field induces open quantum system dynamics, we also show that the results provided by the information-time bounds are in very good agreement with the Kofman-Kurizki universal formula describing decoherence processes. Finally, we numerically test the scaling of the control accuracy as a function of the noise parameters, by means of the dressed chopped random basis (dCRAB) algorithm for quantum optimal control.

Witnessing non-Markovianity by quantum quasi-probability distributions

We employ frames consisting of rank-one projectors (i.e. pure quantum states) and their induced informationally complete quantum measurements to represent generally mixed quantum states by quasi-probability distributions. In the case of discrete frames on finite dimensional systems this results in a vector like representation by quasi-probability vectors, while for the continuous frame of coherent states in continuous variable (CV) systems the approach directly leads to the celebrated representation by Glauber–Sudarshan P-functions and Husimi Q-functions. We explain that the Kolmogorov distances between these quasi-probability distributions lead to upper and lower bounds of the trace distance which measures the distinguishability of quantum states. We apply these results to the dynamics of open quantum systems and construct a non-Markovianity witness based on the Kolmogorov distance of the P- and Q-functions. By means of several examples we discuss the performance of this witness and demonstrate that it is useful in the regime of high entropy states for which a direct evaluation of the trace distance is typically very demanding. For Gaussian dynamics in CV systems we even find a suitable non-Markovianity measure based on the Kolmogorov distance between the P-functions which can alternatively be used as a witness for non-Gaussianity.

Initial correlations in open quantum systems: constructing linear dynamical maps and master equations

We investigate the dynamics of open quantum systems which are initially correlated with their environment. The strategy of our approach is to analyze how given, fixed initial correlations modify the evolution of the open system with respect to the corresponding uncorrelated dynamical behavior with the same fixed initial environmental state, described by a completely positive dynamical map. We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system which acts like the proper dynamical map on the set of physical states and represents its unique linear extension. Furthermore, we demonstrate that this construction leads to a linear, time-local quantum master equation with generalized Lindblad structure involving time-dependent, possibly negative transition rates. Thus, the general non-Markovian dynamics of an open quantum system can be described by means of a time-local master equation even in the case of arbitrary, fixed initial system–environment correlations. We present some illustrative examples and explain the relation of our approach to several other approaches proposed in the literature.