Nonintegrable Systems Research Articles

Productivity and cost of energy chipping with non-integrated harvesting systems in the Coastal Plain of the US south

ABSTRACT Research from the 1980s–2010s suggested that integrated harvesting systems that harvest conventional products (e.g., sawtimber, pulpwood) and energy chips simultaneously were the most effective solution to produce energy chips in the US South. Alternatives, such as biomass-only systems, have important advantages in forest stands with low volumes of merchantable timber. The goal of this study was to estimate the productivity and cost of producing energy chips using non-integrated systems. Innovative chipping contractors using non-integrated systems were identified through contacts with procurement foresters responsible for purchasing energy chips. Elemental time-and-motion studies were conducted to estimate harvesting productivity on five operations, including one clearcut harvest and four first thinnings in overstocked stands. The hourly cost of equipment was estimated using the machine rate method. Cost per tonne was estimated by combining hourly productivity and hourly costs in a modified version of the Auburn Harvesting Analyzer. System productivity averaged 37 tonnes per scheduled machine hour (smh) and cut-and-haul costs averaged $33.86 t−1 (USD), which was comparable to previous estimates from integrated systems. This study suggests there are viable alternatives to integrated harvesting systems to produce energy chips, especially in stands with low volumes of merchantable timber.

Optimizing the role of pharmacists at the primary healthcare centres in Indonesia through an integrated information system

IntroductionThe role of pharmacists at primary healthcare centers (PHCs) in Indonesia still needs long-term improvement. Enhancing interprofessional collaboration through data-driven collaboration is essential to strengthening cooperation. This study aimed to identify the need for an integrated information system to enhance the role of pharmacists at PHCs in Indonesia.MethodsA desk review was applied as the initial step to analyze the role of pharmacists at the PHCs in Indonesia. Furthermore, a qualitative study was conducted using Walt and Gilson’s health policy analysis framework. Semi-structured interviews were conducted in four sections (context, content, process, and actors) with consideration of selected key respondents. All interviews were transcribed verbatim and then analyzed using Braun and Clarke’s thematic analyses, ensuring a comprehensive understanding of the situation.ResultsWe identified two significant challenges in optimizing the use of integrated systems at the PHCs to increase the role of pharmacists. Considering context-content-process-actors, implementing integrated pharmaceutical care standards relies significantly on human resources and infrastructures. Key challenges related to human resources are a limited number of human resources, a high workload, and insufficient use of working tools. We found several challenges regarding infrastructure, such as network connectivity issues, non-integrated systems or applications, and suboptimal benefits from the current systems.ConclusionVarious systems or applications in PHC involve reporting to the Ministry of Health, but detailed integration of these systems needs to be achieved immediately. According to informants, the criteria for desired applications are crucial to optimizing the integrated system, using it, and streamlining tasks for pharmacists at PHCs. Common expectations include an integrated system for monitoring drug usage and orders. Apart from usefulness, network connectivity must be assured for accessibility by all parties.

Thermalization in Krylov basis

We study thermalization in closed non-integrable quantum systems using the Krylov basis. We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific tridiagonal form with all other elements in the matrix being exponentially small, reminiscent of the eigenstate thermalization hypothesis. Within this framework, we propose that the nature of thermalization, whether weak or strong, can be examined by the infinite time average of the Krylov complexity. Moreover, we analyze the variance of Lanczos coefficients as another probe for the nature of thermalization. One observes that although the variance of Lanczos coefficients may capture certain features of thermalization, it is not as effective as the infinite time average of complexity.

Solar-Driven Thermally Regenerative Electrochemical Cells for Continuous Power Generation with Coupled Optical and Thermal Integration.

This study presents the development of a solar-driven thermally regenerative electrochemical cell (STREC) for continuous power generation. Key innovations include dual-function carbon-based electrodes for efficient solar absorption and electrochemical reactions, a transparent and ultrainsulating silica aerogel to maximize solar spectrum transmission while minimizing heat loss, and a compact heat exchanger to recover heat from hot cell streams. Under 1 sun conditions, the STREC achieves a power density of 912.1 mW/m2, doubling the performance compared to a nonintegrated system. At higher solar concentrations (2 suns), the power density further increases to 1214.4 mW/m2. Our findings indicate that this combination holds significant promise for efficient and continuous solar power generation. The application of state-of-the-art redox couples with high-temperature coefficients suggests a potential solar electricity efficiency of 12.6%, comparable to that of industrial photovoltaic technologies, providing a viable pathway for enhancing the renewable energy share in the global energy mix.

Classical and Bohmian Trajectories in Integrable and Nonintegrable Systems

In the present paper, we study both classical and quantum Hénon–Heiles systems. In particular, we make a comparison between the classical and quantum trajectories of integrable and nonintegrable Hénon–Heiles Hamiltonians. From a classical standpoint, we study both theoretically and numerically the form of invariant curves in the Poincaré surfaces of section for several values of the coupling parameter in the integrable case and compare them with those in the nonintegrable case. Then, we examine the corresponding Bohmian trajectories, and we find that they are chaotic in both cases, but with chaos emerging at different times.

Evaluating Growth Performance and Economic Efficiency of Indian Major Carps in Integrated Fish-duck Farming Systems

The experiment was conducted in three villages in Namakkal district to evaluate the effects of an integrated fish-duck farming system on the physico-chemical and biological parameters of pond ecosystems, as well as on overall fish production. This eight-month trial took place from July 2016 to February 2017. Ponds were stocked with fingerlings at a density of 6,000 per hectare, using Indian major carps like Catla (Catla catla), Rohu (Labeo rohita), and Mrigala (Cirrhinus mrigala) in a 4:3:3 ratio to maximize energy utilization through polyculture. Indian Runner ducks (Anas platyrhynchos) were included in the system to provide meat and naturally fertilize the ponds through excreta while grazing freely. In this village-based cultural practice, fish were not given supplementary feed. Instead, the ducks were fed with household food scraps and agricultural by-products, such as broken cereal grains and rice bran, which are readily available in rural areas. The study revealed that water quality parameters such as pH, dissolved oxygen, and alkalinity were significantly higher in the integrated ponds compared to control ponds (without ducks). Additionally, plankton levels (both phytoplankton and zooplankton) improved markedly in the integrated ponds. The Indian major carps in the integrated ponds also achieved better body weight than those in the control ponds. This improved growth rate contributed to a yield of 8,928 kg/ha/year in the integrated system, compared to 5,145 kg/ha/year in the control ponds. These results demonstrate that integrated fish-duck farming is more profitable than non-integrated systems (control) under rural conditions in Tamil Nadu, as it yields higher fish production without additional inputs.

Discrete Time Crystals in Unbounded Potentials.

Discrete time crystalline phases have attracted significant theoretical and experimental attention in the last few years. Such systems require a seemingly impossible combination of nonadiabatic driving and a finite-entropy long-time state, which, surprisingly, is possible in nonergodic systems. Previous works have often relied on disorder for the required nonergodicity; here, we describe the construction of a discrete time crystal (DTC) phase in nondisordered, nonintegrable Ising-type systems. After discussing the conditions for interacting and periodically driven systems to display such phases in general, we propose a concrete model and then provide approximate analytical arguments and direct numerical evidence that it satisfies the conditions and displays a DTC phase robust to local periodic perturbations.

Exact Thermal Eigenstates of Nonintegrable Spin Chains at Infinite Temperature.

The eigenstate thermalization hypothesis (ETH) plays a major role in explaining thermalization of isolated quantum many-body systems. However, there has been no proof of the ETH in realistic systems due to the difficulty in the theoretical treatment of thermal energy eigenstates of nonintegrable systems. Here, we write down analytically thermal eigenstates of nonintegrable spin chains. We consider a class of theoretically tractable volume-law states, which we call entangled antipodal pair (EAP) states. These states are thermal, in the most fundamental sense that they are indistinguishable from the Gibbs state with respect to all local observables, with infinite temperature. We then identify Hamiltonians having the EAP state as an eigenstate and rigorously show that some of these Hamiltonians are nonintegrable. Furthermore, a thermal pure state at an arbitrary temperature is obtained by the imaginary time evolution of an EAP state. Our results offer a potential avenue for providing a provable example of the ETH.

Addressing the non-perturbative regime of the quantum anharmonic oscillator by physics-informed neural networks

Abstract The use of deep learning in physical sciences has recently boosted the ability of researchers to tackle physical systems where little or no analytical insight is available. Recently, the Physics−Informed Neural Networks (PINNs) have been introduced as one of the most promising tools to solve systems of differential equations guided by some physically grounded constraints. In the quantum realm, such an approach paves the way to a novel approach to solve the Schrödinger equation for non-integrable systems. By following an unsupervised learning approach, we apply the PINNs to the anharmonic oscillator in which an interaction term proportional to the fourth power of the position coordinate is present. We compute the eigenenergies and the corresponding eigenfunctions while varying the weight of the quartic interaction. We bridge our solutions to the regime where both the perturbative and the strong coupling theory work, including the pure quartic oscillator. We investigate systems with real and imaginary frequency, laying the foundation for novel numerical methods to tackle problems emerging in quantum field theory.

Superdiffusive to ballistic transport in nonintegrable Rydberg simulator

A common wisdom posits that transport of conserved quantities across clean nonintegrable quantum systems at high temperatures is diffusive when probed from the emergent hydrodynamic regime. We show that this empirical paradigm may alter if the strong interaction limit is taken. Using Krylov-typicality and purification matrix-product-state methods, we establish in short-to-intermediate time scales the following observations for the nonintegrable lattice model imitating the experimental Rydberg blockade simulator. Given the strict projection owing to the infinite density-density repulsion V, the Rydberg chain’s energy transport in the presence of a transverse field g is tentatively superdiffusive at infinite temperature featured by an anomalous scaling exponent 34\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{3}{4}$$\\end{document}, indicating the potential existence of a novel dynamical universality class. Imposing, in addition, a growing longitudinal field h causes a putative superdiffusion-to-ballistic transport transition at h ≈ g. Interestingly, all the above results persist for large but finite interactions and temperatures, provided that the strongly interacting condition g, h ≪ kBT ≪ V is fulfilled. Our predictions are testable by current Rydberg quantum simulation facilities.

Random matrix theory approach to quantum Fisher information in quantum ergodic systems.

We theoretically investigate quantum parameter estimation in quantum chaotic systems. Our analysis is based on an effective description of quantum ergodic systems in terms of a random matrix Hamiltonian. Based on this approach, we derive an analytical expression for the time evolution of the quantum Fisher information (QFI), which we find to have three distinct timescales. Initially, the QFI increase is quadratic in time, characterizing the timescale over which initial information is extractable from local measurements only. This quickly passes into linear increase with slope determined by the decay rate of the measured spin observable. When the information is fully spread among all degrees of freedom, a second quadratic timescale determines the long-time behavior of the QFI. We test our random matrix theory prediction with the exact diagonalization of a nonintegrable spin system, focusing on the estimation of a local magnetic field by measurements of the many-body state. Our numerical calculations agree with the effective random matrix theory approach and show that the information on the local Hamiltonian parameter is distributed throughout the quantum system during the quantum thermalization process.

Two mass-imbalanced atoms in a hard-wall trap: Deep learning integrability of many-body systems.

The study of integrable systems has led to significant advancements in our understanding of many-body physics. We design a series of numerical experiments to analyze the integrability of a mass-imbalanced two-body system through energy-level statistics and deep learning of wave functions. The level spacing distributions are fitted by a Brody distribution and the fitting parameter ω is found to separate the integrable and nonintegrable mass ratios by a critical line ω=0. The convolutional neural network built from the probability density images could identify the transition points between integrable and nonintegrable systems with high accuracy, yet in a much shorter computation time. A brilliant example of the network's ability is to identify a new integrable mass ratio 1/3 by learning from the known integrable case of equal mass, with a remarkable network confidence of 98.22%. The robustness of our neural networks is further enhanced by adversarial learning, where samples are generated by standard and quantum perturbations mixed in the probability density images and the wave functions, respectively.

Fluctuation-dissipation theorem and entanglement dynamics in one-dimensional low-density Jaynes-Cummings Hubbard model after a quench.

In one-dimensional low-density Jaynes-Cummings Hubbard (JCH) models [Phys. Rev. E 106, 064107 (2022)2470-004510.1103/PhysRevE.106.064107], we proved that the eigenstate thermalization hypothesis (ETH) is valid when the tunneling strength and coupling strength are of the same order. Surprisingly, at the weak tunneling limit, we observed that the entanglement entropy and scaling law of kinetic energy operators also exhibit obvious quantum chaotic properties, this is an unexpected result. To substantiate these findings, we further discuss their nonequilibrium dynamics in this paper. Our analysis reveals that when the model is a weak tunneling limit after the quench and the initial state is an equilibrium state of chaos, the system reaches an equilibrium state. This observation supports the conclusion that the low-density JCH model at the weak tunneling limit is nonintegrable, corroborating our previous results [Phys. Rev. E 106, 064107 (2022)2470-004510.1103/PhysRevE.106.064107]. Additionally, by discussing the validity of the fluctuation-dissipation theorem (FDT) and the evolution behavior of entanglement entropy and fidelity, we numerically demonstrate the differences between the one-dimensional low-density JCH model and general nonintegrable systems. Specifically, in the low-density JCH model, when the Hamiltonian after the quench is integrable, the validity of FDT depends on the thermal behavior of the initial Hamiltonian, and a metastable state is observed during the evolution of entanglement entropy. Our research presents an an intriguing and unique nonintegrable model, enriching the current understanding of nonintegrable systems.

Using Lagrangian descriptors to calculate the Maslov index of periodic orbits.

The Maslov index of a periodic orbit is an important piece in the semiclassical quantization of nonintegrable systems, while almost all existing techniques that lead to a rigorous calculation of this index are elaborate and mathematically demanding. In this paper, we describe a straightforward technique, for systems with two degrees of freedom, based on the Lagrangian descriptors. Our method is illustrated by applying it to the two-dimensional coupled quartic oscillator.

Towards continuity: Universal frequency-preserving KAM persistence and remaining regularity in nearly non-integrable Hamiltonian systems

Towards continuity: Universal frequency-preserving KAM persistence and remaining regularity in nearly non-integrable Hamiltonian systems

Lindblad dynamics from spatio-temporal correlation functions in nonintegrable spin- 1/2 chains with different boundary conditions

We investigate the Lindblad equation in the context of boundary-driven magnetization transport in spin-1/2 chains. Our central question is whether the nonequilibrium steady state of the open system, including its buildup in time, can be described on the basis of the dynamics in the closed system. To this end, we rely on a previous study [Heitmann , ], in which a description in terms of spatio-temporal correlation functions was suggested in the case of weak driving and small system-bath coupling. Because this work focused on integrable systems and periodic boundary conditions, we here extend the analysis in three directions: (1) We consider nonintegrable systems, (2) we take into account open boundary conditions and other bath-coupling geometries, and (3) we provide a comparison to time-evolving block decimation. While we find that nonintegrability plays a minor role, the choice of the specific boundary conditions can be crucial due to potentially nondecaying edge modes. Our large-scale numerical simulations suggest that a description based on closed-system correlation functions is a useful alternative to already existing state-of-the-art approaches. Published by the American Physical Society 2024

Krylov complexity as an order parameter for deconfinement phase transitions at large N

Krylov complexity has been proposed as a diagnostic of chaos in non-integrable lattice and quantum mechanical systems, and if the system is chaotic, Krylov complexity grows exponentially with time. However, when Krylov complexity is applied to quantum field theories, even in free theory, it grows exponentially with time. This exponential growth in free theory is simply due to continuous momentum in non-compact space and has nothing to do with the mass spectrum of theories. Thus by compactifying space sufficiently, exponential growth of Krylov complexity due to continuous momentum can be avoided. In this paper, we propose that the Krylov complexity of operators such as O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document} = Tr[FμνFμν] can be an order parameter of confinement/deconfinement transitions in large N quantum field theories on such a compactified space. We explicitly give a prescription of the compactification at finite temperature to distinguish the continuity of spectrum due to momentum and mass spectrum. We then calculate the Krylov complexity of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4, 0 SU(N) Yang-Mills theories in the large N limit by using holographic analysis of the spectrum and show that the behavior of Krylov complexity reflects the confinement/deconfinement phase transitions through the continuity of mass spectrum.

Summability of Transseries Solution of Non-integrable Hamiltonian System

This paper studies the summability of the transseries solution of a nonintegrable Hamiltonian system. Since our system has a resonance and is not integrable a general transseries theory does not work well as far as the author knows. In order to construct a formal transseries solution and prove its summability our main idea is to use the superintegrability of a Hamiltonian system in a class of transseries. More precisely we first show the superintegrability of a Hamiltonian system in the category of transseries via the key Lemmas 1 and 4 which follow. By virtue of the superintegrability we show the existence of a formal transseries solution. Then its summability is proved via the superintegrability. We note that the argument based on the superintegrability is elementary.

Quantum dynamics of a fully blockaded Rydberg atom ensemble

Classical simulation of quantum systems plays an important role in the study of many-body phenomena and in the benchmarking and verification of quantum technologies. Exact simulation is often limited to small systems because the dimension of the Hilbert space increases exponentially with the size of the system. For systems that possess a high degree of symmetry, however, classical simulation can reach much larger sizes. Here we consider an ensemble of strongly interacting atoms with permutation symmetry, enabling the computation of certain collective observables for hundreds of atoms at arbitrarily long evolution times. The system is realized by an ensemble of three-level atoms, where one of the levels corresponds to a highly excited Rydberg state. In the limit of all-to-all Rydberg blockade, the Hamiltonian is invariant under permutation of the atoms. Using techniques from representation theory, we construct a block-diagonal form of the Hamiltonian, where the size of the largest block increases only linearly with the system size. We apply this formalism to derive efficient pulse sequences to prepare arbitrary permutation-invariant quantum states. Moreover, we study the quantum dynamics following a quench, uncovering a parameter regime in which the system thermalizes slowly and exhibits pronounced revivals. Our results create opportunities for the experimental and theoretical study of large interacting and nonintegrable quantum systems. Published by the American Physical Society 2024

An integrated multi-resolution framework for jointly estimating crash type and crash severity

The current research effort contributes to safety literature by developing an integrated framework that allows for the influence of independent variables from crash type and severity components at the disaggregate level to be incorporated within the aggregate level propensity to estimate crash frequency by crash type and severity. The empirical analysis is based on the crash data drawn from the city of Orlando, Florida for the year 2019. The disaggregate level analysis uses 15,518 crash records of three crash types including rear end, angular and sideswipe. Each crash record contains crash specific factors, driver and vehicle factors, roadway attributes, road environmental and weather information. For aggregate level model analysis, the study aggregates the crash records by crash type over 300 traffic analysis zones. An exhaustive set of independent variables including roadway and traffic characteristics, land-use attributes, built environment and sociodemographic factors are considered in this level. The empirical analysis is further augmented by employing several goodness of fit and predictive measures. A validation exercise is also conducted using a holdout sample to highlight the superiority of the proposed integrated model relative to the non-integrated model system. The proposed framework can also incorporate unobserved heterogeneity in the model system. The findings of the study indicate that the proposed framework is advantageous for capturing the variable effects simultaneously across the aggregate and disaggregate levels.