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A classical model of the Schrodinger's wave packet is considered. The problem of finding the energy levels corresponds to a classical manipulation game. It leads to an approximate but non-perturbative method of finding the eigenvalues, exploring the bifurcations of classical trajectories. The role of squeezing turns out decisive in the generation of the discrete spectra.
Conductivity of insulating materials is a key parameter to determine how accumulated charge will distribute across the spacecraft and how rapidly charge imbalance will dissipate. Classical ASTM and IEC methods to measure thin film insulator conductivity apply a constant voltage to two electrodes around the sample and measure the resulting current for tens of minutes. However, conductivity is more appropriately measured for spacecraft charging applications as the "decay" of charge deposited on the surface of an insulator. Charge decay methods expose one side of the insulator in vacuum to sequences of charged particles, light, and plasma, with a metal electrode attached to the other side of the insulator. Data are obtained by capacitive coupling to measure both the resulting voltage on the open surface and emission of electrons from the exposed surface, as well monitoring currents to the electrode. Instrumentation for both classical and charge storage decay methods has been developed and tested at Jet Propulsion Laboratory (JPL) and at Utah State University (USU). Details of the apparatus, test methods and data analysis are given here. The JPL charge storage decay chamber is a first-generation instrument, designed to make detailed measurements on only three to five samples at a time. Because samples must typically be tested for over a month, a second-generation high sample throughput charge storage decay chamber was developed at USU with the capability of testing up to 32 samples simultaneously. Details are provided about the instrumentation to measure surface charge and current; for charge deposition apparatus and control; the sample holders to properly isolate the mounted samples; the sample carousel to rotate samples into place; the control of the sample environment including sample vacuum, ambient gas, and sample temperature; and the computer control and data acquisition systems. Measurements are compared here for a number of thin film insulators using both methods at both facilities. We have found that conductivity determined from charge storage decay methods is 102 to 104 larger than values obtained from classical methods. Another Spacecraft Charging Conference presentation describes more extensive measurements made with these apparatus. This work is supported through funding from the NASA Space Environments and Effects Program and the USU Space Dynamics Laboratory Enabling Technologies Program.
"The escalating impact of climate change induced extreme weather events in urban, suburban, and rural environments demands a rethink of how we have been using the single event-based or use-case-based knowledge graph models. The lack of representation in interaction within environmental variables found in literature led to the development of a novel framework that reflects the true nature of the interconnectedness in our environment. We propose an Environmental Interaction Knowledge Graph (EIKG) framework. This general EIKG framework works as the basis for interconnected environmental events by knitting interrelated events such as hurricanes leading to storm surges, which lead to flood events that could cause mudslides, landslides, etc., The cascading nature of one event leading to another related event in the environment requires an adequate understanding of each event using contextual information before conducting any data-driven analytics. This vision paper showcases how the EIKG:floods, EIKG:wildfire EIKG:landslides, etc, can be derived from a base case framework of EIKG as those individual events are interconnected with some common denominator variables. As an example, the precipitation variable is used in the flood case study as well as in the wildfire case study, as excessive precipitation levels lead to floods, and lack of precipitation leads to droughts and wildfires. We identify the precipitation variable as a “common-denominator-variable” in extreme weather events that play a key role in modeling the environment leading to different extreme weather events based on the variability of that variable (varying values where low precipitation leads to drought, and high values lead to floods). We use the insights gained from EIKG to conduct classical and Quantum Machine Learning (QML) based data analysis on the research questions developed. Our preliminary study shows how the Variational Quantum Classifier (VQC) and Quantum Support Vector Classifier (QSVC) are used along with the classical machine learning models to compare the model accuracies. Our study elaborates on how a quantitative analysis uses state-of-the-art machine learning techniques that include implementing both classical and quantum machine learning models and developing the knowledge graph. The EIKG is used to organize heterogeneous datasets and integrate the relations to case-specific extreme weather events such as floods. The study uses datasets such as county-to-country residential mobility data, socioeconomic datasets from the US Census Bureau, climate and weather-related Earth Observational data from NASA, and critical infrastructure data from the Homeland Infrastructure datasets."
In the United States, manufacturing facilities account for about 32% of total domestic energy consumption in 2014. Robust energy tracking methodologies are critical to understanding energy performance in manufacturing facilities. Due to its simplicity and intuitiveness, the classic energy intensity method (i.e. the ratio of total energy use over total production) is the most widely adopted. However, the classic energy intensity method does not take into account the variation of other relevant parameters (i.e. product type, feed stock type, weather, etc.). Furthermore, the energy intensity method assumes that the facilities’ base energy consumption (energy use at zero production) is zero, which rarely holds true. Therefore, it is commonly recommended to utilize regression models rather than the energy intensity approach for tracking improvements at the facility level. Unfortunately, many energy managers have difficulties understanding why regression models are statistically better than utilizing the classic energy intensity method. While anecdotes and qualitative information may convince some, many have major reservations about the accuracy of regression models and whether it is worth the time and effort to gather data and build quality regression models. This paper will explain why regression models are theoretically and quantitatively more accurate for tracking energy performance improvements. Based on the analysis of data from 114 manufacturing plants over 12 years, this paper will present quantitative results on the importance of utilizing regression models over the energy intensity methodology. This paper will also document scenarios where regression models do not have significant relevance over the energy intensity method.
In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or Hamiltonian formulation of general relativity allows for classical states that do not satisfy the full set of Einstein's equations. This amounts to loosening the Hamiltonian and momentum constraints that are imposed on the initial state. Nevertheless, the quantum theory permits gauge invariant time evolution of these states. The time evolution of these states is such that at the classical level the full set of Einstein's equations would appear to hold, with the physical effects of these states being attributable to an auxiliary, covariantly conserved energy-momentum tensor with no internal degrees of freedom. We derive the generalized Einstein equations for these states and show that a homogeneous and isotropic initial background state contributes to expansion identical to cold dark matter. The inhomogeneous components of this state could source curvature perturbations that grow linearly at linear order. This auxiliary contribution to Einstein's equations could have either sign and thus provide a trivial way to violate the null energy condition, enabling novel gravitational dynamics such as cosmic bounces and wormholes.
High-performance computing systems are rapidly evolving into heterogeneous platforms that fuse quantum accelerators with traditional classical processing units (CPUs) and graphical processing units (GPUs). This convergence calls for runtimes capable of managing both classical and quantum workloads in a unified manner. We introduce an intelligent, task-based runtime that marries the Intelligent RuntIme System (IRIS) asynchronous scheduler with a quantum programming stack through the Quantum Intermediate Representation Execution Engine (QIR-EE). Our design allows programs written in the quantum intermediate representation (QIR) to be dispatched concurrently to a variety of back-ends, including multiple quantum simulators and nascent quantum processors, enabling genuine hybrid execution on a single node. To illustrate its practicality, we partition a 4-qubit and 20-qubit circuit into three sub-circuits using quantum circuit cutting via the QCut library. Each sub-circuit is simulated independently by the QIR-EE driver within IRIS, after which a classical post-processing step merges the simulation results to recover the outcome of the original full-circuit computation. This case study demonstrates how finer task granularity can enable the parallel execution and lower the simulation burden per quantum task while preserving overall accuracy, highlighting the feasibility of our hybrid approach.
In classical dynamical systems, stochastic feedback can stabilize otherwise unstable periodic orbits, giving rise to distinct controlled and uncontrolled phases as the rate of control application is varied. In this work, we apply these control protocols in classical, semiclassical, and quantum regimes to the kicked top, a paradigmatic model of quantum chaos. The quantum kicked top, modeled as the dynamics of a spin-S object, naturally interpolates between these regimes with the spin size S acting as an effective Planck constant. We show that the dynamics of the kicked top in classical, semiclassical, and fully quantum limits can all be controlled using stochastic feedback protocols. Comparing the full quantum dynamics to a truncated Wigner approximation that captures quantum noise but neglects interference beyond the Ehrenfest time, we find that low-moment observables are largely accounted for semiclassically, while the remaining discrepancy in higher moments is consistent with contributions from interference and possibly nonlinearities in rare trajectories that explore the compact phase space. We also find rapid purification in the numerics studied for all rates of control considered, suggesting that control quenches the top's ability to encode a qubit of quantum information even in the uncontrolled phase.
A second-quantization treatment of the solution of the equation of classical mechanics is carried out. It is shown that all of the information about the multiparticle process of creation of a pair of scalar particles by a nonstationary potential barrier is contained in the solutions of Newton’s one-particle equation. The corresponding solution does not depend on Planck’s constant. It is shown that for any spatial quantum problem there exists a temporal classical analog. The obtained results can be used in quantum geometrodynamics.
We study the classical 1D Heisenberg spin glasses in the framework of nearest-neighboring model. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from the first principles of classical mechanics lead to ℕℙ hard problem, that however in the limit of the statistical equilibrium can be calculated by ℙ algorithm. For the partition function of the ensemble a new representation is offered in the form of one-dimensional integral of spin-chains’ energy distribution.
Hybrid quantum–classical systems are emerging as key platforms in quantum computing, sensing, and communication technologies, but the quantum–classical interface (QCI)—the boundary enabling these systems—introduces unique and largely unexplored security vulnerabilities. This position paper proposes using entropy-based metrics to monitor and enhance security, specifically at the QCI. We present a theoretical security outline that leverages well-established information-theoretic entropy measures, such as Shannon entropy, von Neumann entropy, and quantum relative entropy, to detect anomalous behaviors and potential breaches at the QCI. By linking entropy fluctuations to scenarios of practical relevance—including quantum key distribution, quantum sensing, and hybrid control systems—we promote the potential value and applicability of entropy-based security monitoring. While explicitly acknowledging practical limitations and theoretical assumptions, we argue that entropy-based metrics provide a complementary approach to existing security methods, inviting further empirical studies and theoretical refinements that can strengthen future quantum technologies.
Quantum Machine Learning (QML) offers a promising paradigm that leverages quantum computing principles to develop efficient and expressive models for learning from complex and structured data. Recent advances in natural language processing (NLP) and artificial intelligence (AI) have demonstrated capabilities in understanding, generating, and reasoning over linguistic and multimodal information. In this work, we present the Quantum Graph Transformer (QGT), a hybrid quantum–classical architecture that extends graph transformer capabilities through quantum self-attention. The QGT models variable-length sentences as token graphs, where both the embedding encoding and the self-attention mechanisms are implemented using parameterized quantum circuits (PQCs), enabling efficient contextual learning with significantly fewer trainable parameters. We train QGT using both fully connected and 𝑘 -nearest-neighbor graph structures and evaluate it on five benchmark sentiment-classification datasets. Experimental results show that QGT consistently achieves higher or comparable accuracy to existing quantum NLP models and outperforms a Classical Graph Transformer (CGT) baseline with identical architecture, achieving 29.4 × fewer parameters while requiring 3–5 × fewer samples to reach comparable performance. These findings highlight the potential of graph-based quantum models as scalable and data-efficient architectures for natural language understanding.
In high energy proton-nucleus collisions, the single- and double-inclusive soft gluon productions at the leading order have been calculated and phenomenologically studied in various approaches for many years. These studies do not take into account the saturation and multiple rescatterings in the field of the proton. The first saturation correction to these leading order results (the terms that are enhanced by the combination \( {\alpha}_s^2{\mu}^2 \) , where μ 2 is the proton’s color charge squared per unit transverse area) has not been completely derived despite recent attempts using a diagrammatic approach. This paper is the first in a series of papers towards analytically completing the first saturation correction to physical observables in high energy proton-nucleus collisions. Our approach is to analytically solve the classical Yang-Mills equations in the dilute-dense regime using the Color Glass Condensate effective theory and compute physical observables constructed from classical gluon fields. In the current paper, the Yang-Mills equations are solved perturbatively in the field of the dilute object (the proton). Next-to-leading order and next-to-next-to-leading order analytic solutions are explicitly constructed. A systematic way to obtain all higher order analytic solutions is outlined.
The double copy relates scattering amplitudes in gauge and gravity theories, and has also been extended to classical solutions. In this paper, we study solutions in three spacetime dimensions, where the double copy may be expected to be problematic due to the absence of propagating degrees of freedom for the graviton, and the lack of a Newtonian limit. In particular, we examine the double copy of a gauge theory point charge. This is a vacuum solution in gauge theory, but leads to a non-vacuum solution in gravity, which we show is consistent with previously derived constraints. Furthermore, we successfully interpret the non-trivial stress-energy tensor on the gravity side as arising from a dilaton profile, and the Newtonian description of a point charge emerges as expected in the appropriate limit. Thus, our results provide a non-trivial cross-check of the classical Kerr-Schild double copy.
Here in this paper we further develop the fluctuating hydrodynamics proposed in a number of ways. We first work out in detail the classical limit of the hydrodynamical action, which exhibits many simplifications. In particular, this enables a transparent formulation of the action in physical spacetime in the presence of arbitrary external fields. It also helps to clarify issues related to field redefinitions and frame choices. We then propose that the action is invariant under a Z2 symmetry to which we refer as the dynamical KMS symmetry. The dynamical KMS symmetry is physically equivalent to the previously proposed local KMS condition in the classical limit, but is more convenient to implement and more general. It is applicable to any states in local equilibrium rather than just thermal density matrix perturbed by external background fields. Finally we elaborate the formulation for a conformal fluid, which contains some new features, and work out the explicit form of the entropy current to second order in derivatives for a neutral conformal fluid.
The double copy procedure relates gauge and gravity theories through color-kinematics replacements, and holds for both scattering amplitudes and in classical contexts. Moreover, it has been shown that there is a web of theories whose scattering amplitudes are related through operations that exchange color and kinematic factors. In this paper, we generalize and extend this procedure by showing that the classical perturbative double copy of pions corresponds to special Galileons. We consider point-particles coupled to the relevant scalar fields, and find the leading and next to leading order radiation amplitudes. By considering couplings motivated by those that would arise from extracting the longitudinal modes of the gauge and gravity theories, we are able to map the non-linear sigma model radiation to that of the special Galileon. We also construct the single copy by mapping the bi-adjoint scalar radiation to the non-linear sigma model radiation through generalized color-kinematics replacements.
Using the framework of nonlinear fluctuating hydrodynamics (NFH), we examine equilibrium spatio-temporal correlations in classical ferromagnetic spin chains with nearest neighbor interactions. In particular, we consider the classical XXZ-Heisenberg spin chain (also known as Lattice Landau–Lifshitz or LLL model) evolving deterministically and chaotically via Hamiltonian dynamics, for which energy and z-magnetization are the only locally conserved fields. For the easy-plane case, this system has a low-temperature regime in which the difference between neighboring spin’s angular orientations in the XY plane is an almost conserved field. According to the predictions of NFH, the dynamic correlations in this regime exhibit a heat peak and propagating sound peaks, all with anomalous broadening. We present a detailed molecular dynamics test of these predictions and find a reasonably accurate verification. Additionally, we find that, in a suitable intermediate temperature regime, the system shows two sound peaks with Kardar-Parisi-Zhang (KPZ) scaling and a heat peak where the expected anomalous broadening is less clear. In high temperature regimes of both easy plane and easy axis case of LLL, our numerics show clear diffusive spin and energy peaks and absence of any sound modes, as one would expect. We also simulate an integrable version of the XXZ-model, for which the ballistic component instead moves with a broad range of speeds rather than being concentrated in narrower peaks around the sound speed.
We carry out the classical analysis of spin–orbit coupling in hydrogen-like atoms, using the modern expressions for the force and energy of an electric/magnetic dipole in an electromagnetic field. We disclose a novel physical meaning of this effect and show that for a laboratory observer the energy of spin–orbit interaction is represented solely by the mechanical energy of the spinning electron (considered as a gyroscope) due to the Thomas precession of its spin. Concurrently we disclose some errors in the old and new publications on this subject. - Highlights: • Classical analysis of spin–orbit coupling in a laboratory frame was erroneous. • Electromagnetic energy of electron in atom does not contribute to spin–orbit coupling. • Spin–orbit splitting results from the energy of Thomas precession of electron spin.
This paper systematically develops the Schrödinger formalism that is valid also for gyrotropic media where the material weights W=( ε χ χ* μ )≠ W-bar are complex. This is a non-trivial extension of the Schrödinger formalism for non- gyrotropic media (where W= W-bar ) that has been known since at least the 1960s (Wilcox, 1966; Kato, 1967). Here, Maxwell’s equations are rewritten in the form i∂{sub t}Ψ=MΨ where the selfadjoint (hermitian) Maxwell operator M=W{sup -1} Rot |{sub ω≥0}=M* takes the place of the Hamiltonian and Ψ is a complex wave representing the physical field (E,H)=2Re Ψ. Writing Maxwell’s equations in Schrödinger form gives us access to the rich toolbox of techniques initially developed for quantum mechanics and allows us to apply them to classical waves. To show its utility, we explain how to identify conserved quantities in this formalism. Moreover, we sketch how to extend our ideas to other classical waves.