System Dynamics Research Articles

Fock-Space Delocalization and the Emergence of the Porter-Thomas Distribution from Dual-Unitary Dynamics

The chaotic dynamics of quantum many-body systems are expected to quickly randomize any structured initial state, delocalizing it in the Fock space. In this Letter, we study the spreading of an initial product state in Hilbert space under dual-unitary dynamics, captured by the inverse participation ratios and the distribution of overlaps (bit-string probabilities). We consider the self-dual kicked Ising model, a minimal model of many-body quantum chaos that can be seen as either a periodically driven Floquet model or a dual-unitary quantum circuit. Both analytically and numerically, we show that the inverse participation ratios rapidly approach their ergodic values, corresponding to those of Haar random states, and establish the emergence of the Porter-Thomas distribution for the overlap distribution. Importantly, this convergence happens exponentially fast in time, with a timescale that is independent of system size. We inspect the effect of local perturbations that break dual unitarity and show a slowdown of the spreading in Fock space, indicating that dual-unitary circuits are maximally efficient at preparing random states. Our Letter establishes bridges between the dynamics of many-body systems and random matrix theory through the time evolution of structured initial states and finds natural applications in demonstrating a quantum advantage in random sampling and in benchmarking quantum devices. Published by the American Physical Society 2025

Dynamical Complexity in Geomagnetically Induced Current Activity Indices Using Block Entropy

Geomagnetically Induced Currents (GICs) are a manifestation of space weather events at ground level. GICs have the potential to cause power failures in electric grids. The GIC index is a proxy of the ground geoelectric field derived solely from geomagnetic field data. Information theory can be used to shed light on the dynamics of complex systems, such as the coupled solar wind–magnetosphere–ionosphere–ground system. We performed block entropy analysis of the GIC activity indices at middle-latitude European observatories around the St. Patrick’s Day March 2015 intense magnetic storm and Mother’s Day (or Gannon) May 2024 superintense storm. We found that the GIC index values were generally higher for the May 2024 storm, indicating elevated risk levels. Furthermore, the entropy values of the SYM-H and GIC indices were higher in the time interval before the storms than during the storms, indicating transition from a system with lower organization to one with higher organization. These findings, including the temporal dynamics of the entropy and GIC indices, highlight the potential of this method to reveal pre-storm susceptibility and relaxation processes. This study not only adds to the knowledge of geomagnetic disturbances but also provides valuable practical implications for space weather forecasting and geospatial risk assessment.

Decoupled level and flow rate control of a two-tank system in beverage production: A comparative analysis of Fuzzy-PID and GA-PID for minimum time operation.

Due to the nonlinear characteristics of the valves and the interactions between the controlled variables, designing a control system for coupled tanks is a difficult task. This paper deals with the comparative study between Fuzzy-PID and GA-PID controllers for decoupling level and flow rate control of two tank systems for beverage factories with minimum time optimal operation. In most process control industries, each process requires multiple control variables. Here two input two output (TITO) systems are considered highly interacting multivariable control systems. The decoupling control scheme (Pre-compensator (dynamic) decoupling) is used to reduce the correlation between the controlled and manipulated variables by diagonalizing the system. The two independent SISO systems are further controlled by different controllers so that the system can trace the set point and yield a good time response. Two radically different control approaches are presented and compared for this system's dynamics, motivated by a desire to provide precise liquid-level control and regulate the flow rate. MATLAB /Simulink model and tuning algorithm (GA) are used for simulation. As the simulation result ensured, the GA-PID controller is the used for the specified system which is based on the transient and steady-state specifications. Quantitatively; the GA-PID controller has 39.167ms rise time, 8.50sec settling time, and -0.393% overshoot; whereas FLC-PID has 118.101ms rise time, 8.65sec settling time, and -0.033% overshoot. But in GA with PID controllers, the external disturbance tolerance capability of the proposed scheme, meaning robustness against external disturbance has a slight difference and FLC-PID has perfectly achieved the robustness. Depending on the result, FLC-PID has more result than GA-PID controller based on the set of specifications. Hence robustness is more important than time performances.

Understanding Ecological Systems Using Knowledge Graphs: An Application to Highly Pathogenic Avian Influenza

Abstract Motivation Ecological systems are complex. Representing heterogeneous knowledge about ecological systems is a pervasive challenge because data are generated from many subdisciplines, exist in disparate sources, and only capture a subset of interactions underpinning system dynamics. Knowledge graphs have been successfully applied to organize heterogeneous data and to predict new linkages in complex systems. Though not previously applied broadly in ecology, knowledge graphs have much to offer in an era when system dynamics are responding to rapid changes across multiple scales. Results We developed a knowledge graph to demonstrate the method’s utility for ecological problems focused on highly pathogenic avian influenza (HPAI), a highly transmissible virus with a broad host range, wide geographic distribution, and rapid evolution with pandemic potential. We describe the development of a graph to include data related to HPAI including pathogen-host associations, species distributions, and population demographics, using a semantic ontology that defines relationships within and between datasets. We use the graph to perform a set of proof-of-concept analyses validating the method and identifying patterns of HPAI ecology. We underscore the generalizable value of knowledge graphs to ecology including ability to reveal previously known relationships and testable hypotheses in support of a deeper mechanistic understanding of ecological systems. Availability and implementation The data and code are available under the MIT License on GitHub at https://github.com/cghss-data-lab/uga-pipp.

Noise-immune zeroing neural dynamics for dynamic signal source localization system and robotic applications in the presence of noise

Time angle of arrival (AoA) and time difference of arrival (TDOA) are two widely used methods for solving dynamic signal source localization (DSSL) problems, where the position of a moving target is determined by measuring the angle and time difference of the signal's arrival, respectively. In robotic manipulator applications, accurate and real-time joint information is crucial for tasks such as trajectory tracking and visual servoing. However, signal propagation and acquisition are susceptible to noise interference, which poses challenges for real-time systems. To address this issue, a noise-immune zeroing neural dynamics (NIZND) model is proposed. The NIZND model is a brain-inspired algorithm that incorporates an integral term and an activation function into the traditional zeroing neural dynamics (ZND) model, designed to effectively mitigate noise interference during localization tasks. Theoretical analysis confirms that the proposed NIZND model exhibits global convergence and high precision under noisy conditions. Simulation experiments demonstrate the robustness and effectiveness of the NIZND model in comparison to traditional DSSL-solving schemes and in a trajectory tracking scheme for robotic manipulators. The NIZND model offers a promising solution to the challenge of accurate localization in noisy environments, ensuring both high precision and effective noise suppression. The experimental results highlight its superiority in real-time applications where noise interference is prevalent.

Associated network family of the unified piecewise linear chaotic family and their relevance

Abstract Duality analysis of time series and complex networks has been a frontier topic during the last several decades. According to some recent approaches in this direction, the intrinsic dynamics of typical nonlinear systems can be better characterized by considering the related nonlinear time series from the perspective of networks science. In this paper, the associated network family of the unified piecewise-linear (PWL) chaotic family, which can bridge the gap of the PWL chaotic Lorenz system and the PWL chaotic Chen system, was firstly constructed and analyzed. We constructed the associated network family via the original and the modified frequency-degree mapping strategy, as well as the classical visibility graph and horizontal visibility graph strategy, after removing the transient states. Typical related network characteristics, including the network fractal dimension, of the associated network family, are computed with change of single key parameter α. These characteristic vectors of the network are also compared with the Largest Lyapunov exponent (LLE) vector of the related original dynamical system. It can be found that, some network characteristics are highly correlated with LLE vector of the original nonlinear system, i.e., there is an internal consistency between the Largest Lyapunov exponents, some typical associated network characteristics, and the related network fractal dimension index. Numerical results show that the modified frequency-degree mapping strategy can demonstrate highest correlation, which means it can behave better to capture the intrinsic characteristics of the unified PWL chaotic family.

Study and circuit design of stochastic resonance system based on memristor chaos induction

Abstract Memristor chaotic research has become a hotspot in the academic world, however, there are few explorations combining memristor and stochastic resonance, and the correlation research between chaos and stochastic resonance is still in the preliminary stage. In this paper, we focus on the stochastic resonance induced by memristor chaos, which enhances the dynamics of chaotic systems through the introduction of memristor and induces the memristor stochastic resonance under certain conditions. Firstly, the memristor chaos model is constructed, and the memristor stochastic resonance model is constructed by adjusting the parameters of the memristor chaos model. Secondly, the combination of dynamics analysis and experimental verification is used to analyze the memristor stochastic resonance and to investigate the trend of the output signal of the system under different amplitudes of the input signal. Finally, the practicality and reliability of the constructed model are further verified through the design and testing of the analogue circuit, which provides a strong support for the practical application of the memristor chaos induced stochastic resonance model.

Tailoring the Electrocatalytic Properties of Porphyrin Covalent Organic Frameworks for Highly Selective Oxygen Sensing In Vivo.

In vivo selective sensing of oxygen (O2) dynamics in the central nervous system could provide insights into energy metabolism and neural activities. Although the electrocatalytic four-electron oxygen reduction reaction (ORR) paves an effective way to the electrochemical sensing of O2 in vivo, the concurrent hydrogen peroxide reduction reaction (HPRR) within the potential windows for four-electron ORR unfortunately poses a great challenge to the conventional mechanism employed for selective electrochemical O2 sensing. In this work, we find that regulation of the linkers within the skeleton of porphyrin-based covalent organic frameworks (COFs) could improve the selectivity of the O2 sensor against hydrogen peroxide (H2O2). The electrochemical results reveal that the Co porphyrin active sites facilitate the direct four-electron pathway for ORR and that the Co porphyrin-based COF, enriched with pyrene units, shows enhanced four-electron ORR kinetics and better tolerance to HPRR. The theoretical calculation suggests that introducing pyrene units essentially weakens the adsorption of H2O2, leading to suppression of the HPRR. The microsensor fabricated with the Co porphyrin-based COF as the electrocatalyst features a high selectivity for real-time monitoring of O2 in a living rat brain.

Non-traditional data to inform modern climate science

The global climate is changing rapidly, with cascading impacts across the world. Even though the modern instrument-based record of Earth observations reflects decades of critical work, multi-century time series may be required to understand and forecast key elements of Earth system dynamics. Here, we review the potential uses of non-traditional climate data records—observations reported without using modern instruments or standardized measurement protocols—to identify climate and ecosystem dynamics that predate modern methodologies and tools. We compile a list of diverse datasets collected over more than 500 years, including landscape paintings, sea lore, and animal migration data. This initial review presents opportunities for further investigation to reconstruct past climate or to use non-traditional records to complement modern instrument methods.

ML-MCTDH-Aid: An auxiliary package for multilayer multiconfiguration time-dependent Hartree calculations.

The multilayer-multiconfiguration time-dependent Hartree (ML-MCTDH) method has garnered significant attention in the realm of theoretical chemistry owing to its powerful ability to perform numerically exact descriptions of multi-dimensional quantum dynamics and exhibit the remarkable performance in simulating the nonadiabatic dynamics of complex systems. Despite the availability of computational packages within the ML-MCTDH framework, executing these calculations seamlessly is not a straightforward task. Typically, substantial efforts are necessitated to configure the correct inputs for ML-MCTDH calculations, which require to correctly define several non-trivial parameters, to reasonably setup the optimal tree expansion of wavefunctions, and to properly select basis function numbers. To address these challenges, we have developed an auxiliary package named ML-MCTDH-Aid, which facilitates the setup of ML-MCTDH calculations using the Heidelberg MCTDH package in a user-friendly manner. This package is primarily tailored to handle the high-dimensional nonadiabatic dynamics governed by the Hamiltonian composed of several electronic states, several vibrational modes and their linear vibronic coupling terms. It automatically generates multiple essential input files, and all the calculations can be performed in an all-in-one black-box easy-to-use manner. To show the utility of the ML-MCTDH-Aid package, we provide a step-by-step tutorial that demonstrates running ML-MCTDH studies on three models. These examples illuminate how the utilization of the ML-MCTDH-Aid package significantly enhances the efficiency and effectiveness of ML-MCTDH calculations. This substantially boosts the accessibility of ML-MCTDH calculations in tackling the high-dimensional quantum dynamics of complex systems.

Decision-making model for production and operation of underground gold mines considering low-carbon condition.

Within the framework of a low-carbon transition and integrated mineral resource exploitation, this study presents an innovative system dynamics (SD) model designed to optimize decision-making and enhance profitability in underground gold mining operations. The novel approach seamlessly integrates critical subsystems, including reserves, mining, ore dressing, smelting, financial, and carbon reduction, offering a comprehensive framework for the analysis of efficiency and sustainability. Utilizing causal loop and system flow diagrams, the model elucidates the synergistic impacts of index variations on mine operational efficiency. The model is applied to a case study involving three mining areas within a specific gold mine in China, where sensitivity analysis identifies key indicators affecting profitability. Furthermore, it examines dynamic trends under varying carbon tax scenarios. The findings reveal that mining strategic adjustments can significantly enhance profitability, extend the operational lifespan of mines, and reduce emissions.

Stirring the false vacuum via interacting quantized bubbles on a 5,564-qubit quantum annealer

Abstract False vacuum decay—the transition from a metastable quantum state to a true vacuum state—plays an important role in quantum field theory and non-equilibrium phenomena such as phase transitions and dynamical metastability. The non-perturbative nature of false vacuum decay and the limited experimental access to this process make it challenging to study, leaving several open questions regarding how true vacuum bubbles form, move and interact. Here we observe quantized bubble formation in real time, a key feature of false vacuum decay dynamics, using a quantum annealer with 5,564 superconducting flux qubits. We develop an effective model that captures both initial bubble creation and subsequent interactions, and remains accurate under dissipation. The annealer reveals coherent scaling laws in the driven many-body dynamics for more than 1,000 intrinsic qubit time units. This work provides a method for investigating false vacuum dynamics of large quantum systems in quantum annealers.

Unveiling Nonlinear Modes of Induced-Charge Electro-Osmosis in AC Electric Fields.

Induced-charge electro-osmosis (ICEO) is prevalent in electrochemistry and micro/nanofluidics, even when subjected to an alternating current (AC) electric field. Previous studies suggest that ICEO primarily occurs near electrodes or ion-selective membranes within a range of tens of microns. In this experimental study, we reveal the existence of additional modes in ICEO driven by an AC electric field. We demonstrate that nonlinear electroosmotic flow (EOF) can occur between two electrodes situated 5 mm apart through long-range electroconvection. Notably, we observe a soliton-like wave of ion concentration fluctuation traveling from the working electrode to the ground electrode, causing significant disruption to the electric triple layer (ETL) on the ground electrode. Consequently, both the ETL structure on the electrodes and the bulk fluid are profoundly influenced by an external electric field. These findings are vital for enhancing the understanding of intrinsic dynamics in electrochemical and energy systems and for the development of novel micro/nanofluidic devices.

Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning

Abstract Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green’s function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff–Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on recurrent neural networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green’s functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green’s functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from O ( N t 3 ) to O ( N t ) where Nt is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

Low-Rank Variational Quantum Algorithm for the Dynamics of Open Quantum Systems

The simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable advantage for the efficient simulation of their static and dynamical properties, thanks to hybrid quantum-classical variational algorithms to approximate the dynamics of the density matrix describing the quantum state in terms of an ensemble average. Here, a variational quantum algorithm is developed to simulate the real-time evolution of the density matrix governed by the Lindblad master equation, under the assumption that the quantum state has a bounded entropy along the dynamics, entailing a low-rank representation of its density matrix. The algorithm encodes each pure state of the statistical mixture as a parametrized quantum circuit, and the associated probabilities as additional variational parameters stored classically, thereby requiring a significantly lower number of qubits than algorithms where the full density matrix is encoded in the quantum memory. Two variational ansatze are proposed, and their effectiveness is assessed in the simulation of the dynamics of a 2D dissipative transverse field Ising model. The results underscore the algorithm's efficiency in simulating the dynamics of open quantum systems in the low-rank regime with limited quantum resources on a near-term quantum device.

Stability analysis of chaotic systems in latent spaces

Abstract Partial differential equations, and their chaotic solutions, are pervasive in the modelling of complex systems in engineering, science, and beyond. Data-driven methods can find solutions to partial differential equations with a divide-and-conquer strategy: The solution is sought in a latent space, on which the temporal dynamics are inferred (“latent-space” approach). This is achieved by, first, compressing the data with an autoencoder, and, second, inferring the temporal dynamics with recurrent neural networks. The overarching goal of this paper is to show that a latent-space approach can not only infer the solution of a chaotic partial differential equation, but it can also predict the stability properties of the physical system. First, we employ the convolutional autoencoder echo state network (CAE-ESN) on the chaotic Kuramoto-Sivashinsky equation for various chaotic regimes. We show that the CAE-ESN (i) finds a low-dimensional latent-space representation of the observations and (ii) accurately infers the Lyapunov exponents and covariant Lyapunov vectors (CLVs) in this low-dimensional manifold for different attractors. Second, we extend the CAE-ESN to a turbulent flow, comparing the Lyapunov spectrum to estimates obtained from Jacobian-free methods. A latent-space approach based on the CAE-ESN effectively produces a latent space that preserves the key properties of the chaotic system, such as Lyapunov exponents and CLVs, thus retaining the geometric structure of the attractor. The latent-space approach based on the CAE-ESN is a reduced-order model that accurately predicts the dynamics of the chaotic system, or, alternatively, it can be used to infer stability properties of chaotic systems from data.

Nonlinear parametric generation of optical vortices and their propagation in graphene quantum dots

In this paper, we investigate the propagation of optical vortices carrying orbital angular momentum in a coherently prepared graphene quantum dot (GQD) system. Using the Maxwell–Bloch equations and assuming weak light–matter interaction, we examine two key scenarios. The first scenario involves the transfer of optical vortices through nonlinear parametric process, starting with one vortex beam absent and then generated during its interaction with the GQD system. We analyze how various system parameters affect vortex conversion efficiency and the matching of optical vortices. Our results reveal that vortex conversion efficiency is significantly influenced by detuning and incoherent pumping, with notable efficiency and steady-state intensity achieved when these parameters are properly manipulated. In the second scenario, where both vortex beams are initially present, we explore their propagation within the GQD medium. In particular, we observe that when both beams are resonant and incoherent pumping is applied, they quickly stabilize and perfectly match over short propagation distances. Conversely, when both beams are nonresonant, they exhibit oscillatory decay in intensity, preventing them from achieving a steady-state match and leading to absorption by the GQD medium. This study enhances our understanding of vortex beam dynamics in GQD systems and provides insights into optimizing vortex beam transfer for high-dimensional quantum information processing applications.

Pancharatnam phase control of atomic ensembles based on quantum memory effects in photonic cavities

In this paper, we explore the manipulation and control of the Pancharatnam phase in atomic ensembles through the utilization of quantum memory effects. By analyzing the time evolution of the excited state population of [Formula: see text]-atoms within a single photonic cavity, we gain insights into the behavior and manipulation of this phase. Numerical simulations of the system exact solution yield density plots illustrating the time evolution of the excited state population and Pancharatnam phase. Our findings demonstrate the potential to control the system dynamics using the Pancharatnam phase in atomic ensembles through quantum memory effects. The observed behaviors and characteristics contribute to our understanding of quantum systems and hold promise for crucial applications in quantum information processing and communication. These results provide valuable insights into the fundamental aspects of the Pancharatnam phase and its control, paving the way for further investigations and applications in quantum optics and information science.

System Failures and the Realities of “Reform”: A Practical Understanding of Decision-Making in Child Welfare

How exactly is the child welfare system failing children? Abolitionist perspectives have centered the failures and harms inherent to and reproduced by the system. Despite voicing disagreement with abolition as a path forward, advocates/proponents of reform have not done the painstaking work of analyzing failures of the system itself. We begin to address this gap by examining the persistent phenomenon of critical thinking errors in child welfare, putting into context how and why the child welfare universe not only fails to ameliorate them but actively creates environments conducive to faulty thinking. We conclude that improving outcomes for families can only be accomplished through honest reckonings with current system dynamics and a radical recalibration in child welfare tolerance for child harm.

Human Rights in Sociopsychological Perspective

Abstract From the standpoint of sociopsychology, we attempt to isolate those aspects of human rights that are distinctly sociopsychological in nature, to later identify them as interindividual segments of social system dynamics. In social perspective, human rights may be viewed as social events and, in a sociopsychological perspective, all social events are conceptualized as social formations of interacting contingencies. Such social formations are constituted of interindividual relations set in a complex of institutional practices. The interindividual relation is conceptualized as a set of contingencies directly affecting individual behavior and has three dimensions: exchange, power, and sanction. Institutions are conceptualized as sociohistorical circumstances having their origins as informal or formal practices. Human rights are addressed in terms of interindividual dimensions and institutional practices constituting specific social formations.