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We study entanglement in a simple model comprising two coupled linear harmonic oscillators of the same natural frequency. The system is separable in the center of mass (COM) and relative coordinates into two oscillators of frequency ωc and ωr. We compute standard entanglement measures (subsystem linear entropy and subsystem von Neumann entropy) as well as several tomographic entanglement indicators (Bhattacharyya distance, Kullback–Leibler divergence, and inverse participation ratio) as functions of the frequency ratio η = ωc/ωr, keeping the COM oscillator in its ground state. We demonstrate that, overall, the entanglement indicators reflect quite faithfully the variations in the standard measures. The entanglement is shown to be minimum at η = 1 and maximum at η → 0 or ∞. [ABSTRACT FROM AUTHOR]

We propose and analyze a universal method to obtain fast charging of a quantum battery by a driven charger system using controlled, pure dephasing of the charger. While the battery displays coherent underdamped oscillations of energy for weak charger dephasing, the quantum Zeno freezing of the charger energy at high dephasing suppresses the rate of transfer of energy to the battery. Choosing an optimum dephasing rate between the regimes leads to a fast charging of the battery. We illustrate our results with the charger and battery modeled by either two-level systems or harmonic oscillators. Apart from the fast charging, the dephasing also renders the charging performance more robust to detuning between the charger, drive, and battery frequencies for the two-level systems case. [ABSTRACT FROM AUTHOR]

Quantum control of a linear oscillator using a static dispersive coupling to a nonlinear ancilla underpins a wide variety of experiments in circuit QED. Extending this control to more than one oscillator while minimizing the required connectivity to the ancilla would enable hardware-efficient multi-mode entanglement and measurements. We show that the spectrum of an ancilla statically coupled to a single mode can be made to depend on the joint photon number in two modes by applying a strong parametric beamsplitter coupling between them. This 'joint-photon number-splitting' regime extends single-oscillator techniques to two-oscillator control, which we use to realize a hardware-efficient erasure check for a dual-rail qubit encoded in two superconducting cavities. This scheme leverages the high-fidelity beamsplitter coupling already required for single- and two-qubit gates while permitting minimal crosstalk between circuit elements. Furthermore, the flexibility to choose the pulse shape allows us to limit the susceptibility to different error channels. We use this scheme to detect leakage errors with a missed erasure fraction of (9.0 ± 0.5) × 10−4 while incurring an erasure rate of 2.92 ± 0.01% and a Pauli error rate of 0.31 ± 0.01%, both of which are dominated by cavity errors. [ABSTRACT FROM AUTHOR]

We report the results of calculations of the linear polarizability and second hyperpolarizability of the H2 molecule in the bond dissociation process. These calculations were performed for isolated molecules, as well as molecules under spatial confinement. The spatial confinement was modeled using the external two-dimensional (cylindrical) harmonic oscillator potential. In contrast to the recently investigated polar LiH molecule, it was shown that the spatial confinement significantly diminishes the linear and nonlinear response of H2 for each interatomic (H-H) distance. [ABSTRACT FROM AUTHOR]

In this paper, we present a "non-linear" factorization of a family of non-normal operators arising from Gribov's theory of the following form: H λ ′ , μ , λ = λ ′ A * 2 A 2 + μ A * A + i λ A * (A + A *) A , where the quartic Pomeron coupling λ ′ , the Pomeron intercept μ and the triple Pomeron coupling λ are real parameters, and i 2 = − 1 . A * and A are, respectively, the usual creation and annihilation operators of the one-dimensional harmonic oscillator obeying the canonical commutation relation [ A , A * ] = I . In Bargmann representation, we have A ⟷ d d z and A * ⟷ z , z = x + i y . It follows that H λ ′ , μ , λ can be written in the following form: H λ ′ , μ , λ = p (z) d 2 d z 2 + q (z) d d z , where p (z) = λ ′ z 2 + i λ z and q (z) = i λ z 2 + μ z. This operator is an operator of the Heun type where the Heun operator is defined by H = p (z) d 2 d z 2 + q (z) d d z + v (z) , where p (z) is a cubic complex polynomial, q (z) and v (z) are polynomials of degree at most 2 and 1, respectively, which are given. For z = − i y , H λ ′ , μ , λ takes the following form: H λ ′ , μ , λ = − a (y) d 2 d y 2 + b (y) d d z , with a (y) = y (λ − λ ′ y) and b (y) = y (λ y + μ). We introduce the change of variable y = λ 2 λ ′ (1 − c o s (θ)) , θ ∈ [ 0 , π ] to obtain the main result of transforming H λ ′ , μ , λ into a product of two first-order operators: H ˜ λ ′ , μ , λ = λ ′ (d d θ + α (θ)) (− d d θ + α (θ)) , with α (θ) being explicitly determined. [ABSTRACT FROM AUTHOR]

In 1925, Heisenberg, Born, and Jordan developed matrix mechanics as a strategy to solve quantum-mechanical problems. While finite-sized matrix formulations are commonly taught in quantum instruction, following the logic and detailed steps of the original matrix mechanics has become a lost art. In preparation for the 100th anniversary of the discovery of quantum mechanics, we present a modernized discussion of how matrix mechanics is formulated, how it is used to solve quantum-mechanical problems, and how it can be employed as the starting point for a postulate-based formulation of quantum-mechanics instruction. We focus on the harmonic oscillator to describe how quantum mechanics advanced from the Bohr–Sommerfeld quantization condition, to matrix mechanics, to the current abstract ladder-operator approach. We also describe a number of different activities that can be included in the quantum mechanics classroom to celebrate this centennial. Editor's Note: The finite spacetime manifold in which outgoing waves reach infinity in a finite spacetime interval was introduced in the 1960s by Roger Penrose. It plays an important role in the analysis of gravitational waves. In this work the author shows how to construct a temporal foliation using spacelike slices with hyperbolic geometry in compactified Minkowski space. Instructors in special relativity will be able to make these ideas accessible to their students, including an application to massless fields in flat spacetime. [ABSTRACT FROM AUTHOR]

In this paper, we provide a glimpse of the original formulation of quantum mechanics (a.k.a. matrix mechanics), as proposed by Heisenberg, Born, and Jordan in 1925, by showing how it solves the quantum harmonic oscillator. This presentation can shed light on the relationship between different formulations and give students a deeper understanding of quantum mechanics. Editor's Note: Introductory quantum mechanics courses typically discuss only the early history of the quantum era, including the experiments that differed from classical predictions, such as black body radiation spectra, and the rough heuristic rules invented to describe these unexpected results, such as the Rydberg formula for atomic emission spectra and Bohr's correspondence principle. This "old quantum theory" built the conceptual foundations that then enabled the development of several complete mathematical formalisms, with matrix mechanics first emerging in 1925, and wave mechanics in 1926. Introductory courses typically skip this history and present only the modern formalism. Here, the arguments of Heisenberg's "magical" 1925 paper that quickly inspired Born and Jordan's matrix mechanics are used to find the energy spectrum of the quantum harmonic oscillator in a presentation appropriate for upper-level undergraduates. [ABSTRACT FROM AUTHOR]

The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all observables in one model, and the observables of the other model. Thus the duality we find, appears to be in conflict with the usual assertion that classical theories can never reproduce quantum effects as observed in many quantum models. We suggest that there must be more of such relationships, but we study only this one as a prototype. It reveals how classical hidden variables may work. The classical states can form the basis of Hilbert space that can be adopted in describing the quantum model. Wave functions in the quantum system generate probability distributions in the classical one. One finds that, where the classical system always obeys the rule probability in = probability out, the same probabilities are quantum probabilities in the quantum system. It is shown how the quantum x and p operators in a quantum oscillator can be given a classical meaning. It is explained how an apparent clash with quantum logic can be rationalized. [ABSTRACT FROM AUTHOR]

This work deals with the key constituent behind the existence of superfluid states in ultracold fermionic gases confined in a harmonic trap in 2D, namely, the formation of Cooper pairs in the presence of a Fermi sea in inhomogeneous confinement. For a set of finite-range models representing particle–particle interaction, we first ascertain the simultaneity of the emergence of bound states and the divergence of the s-wave scattering length in 2D as a function of the interaction potential parameters in free space. Then, through the analysis of two particles interacting in 2D harmonic confinement, we evaluate the energy shift with respect to the discrete harmonic oscillator levels for both repulsive and attractive cases. All of these results are the basis for determining the energy gaps of Cooper pairs arising from two particles interacting in the presence of a Fermi sea consisting of particles immersed in a 2D harmonic trap. [ABSTRACT FROM AUTHOR]

The molecular characteristics and rheological properties of three UHMWPE samples were investigated. The high-temperature GPC method was used for characterizing UHMWPE samples used. The interpretation of the measurement results was based on calibration using the PS standard and the approximation of the PS data by linear and cubic polynomials, as well as on the data for linear PE. The assessment of the average MW and MWD depends on the choice of calibration method, so that different methods give different results. Only the results obtained using PS with cubic approximation are close to the characteristics offered by the manufacturer. It was also shown that the obtained MW characteristics depend on the dissolution time. The reason for this may be the presence of any processing-aid compounds or destruction of macromolecules. Measurements of the rheological properties were performed in creep modes for a wide range of shear stresses and harmonic oscillations. It was shown that even at 210 °C, UHMWPE does not flow, and the observed irreversible deformations are due to the plasticity of the polymer, i.e., UHMWPE is in an elastic–plastic state. The ultimate plastic deformations drop sharply with increasing MW of the polymer. The plasticity modulus for the highest molecular weight UHMWPE samples does not depend on stress. Measurements of viscoelastic characteristics confirmed that the terminal region of viscous flow cannot be reached under any conditions. Increasing the duration of holding the polymer at high temperature leads not to flow, but to the destruction of macromolecules. [ABSTRACT FROM AUTHOR]

We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and fermionic generators. The algebraic structure thus obtained corresponds to a deformed Grassmann-type algebra, involving anticommuting Grassmann-type variables. The role played by the latter in implementing gauge invariance in second quantization within our procedure is then discussed. This discussion includes the application of the mapping to the case of the bosonic and fermionic harmonic oscillator Hamiltonians. [ABSTRACT FROM AUTHOR]

Most physical systems, whether classical or quantum mechanical, exhibit spherical symmetry. Angular momentum, denoted as ℓ , is a conserved quantity that appears in the centrifugal potential when a particle moves under the influence of a central force. This study introduces a formalism in which ℓ plays a unifying role, consolidating solvable central potentials into a superpotential. This framework illustrates that the Coulomb potential emerges as a direct consequence of a homogeneous (r-independent) isotropic superpotential. Conversely, an ℓ -independent central superpotential results in a 3-dimensional harmonic oscillator (3-DHO) potential. Moreover, a local ℓ -dependent central superpotential generates potentials applicable to finite-range interactions such as molecular or nucleonic systems. Additionally, we discuss generalisations to arbitrary D dimensions and investigate the properties of the superpotential to determine when supersymmetry is broken or unbroken. This scheme also shows that the free-particle wave function in three dimensions is obtained from the spontaneous breakdown of supersymmetry and clarifies how a positive 3-DHO potential, as an upside-down potential, can have a negative energy spectrum. We also present complex isospectral deformations of the central superpotential and superpartners, which can have interesting applications for open systems in dynamic equilibrium. Finally, as a practical application, we apply this formalism to specify a new effective potential for the deuteron. [ABSTRACT FROM AUTHOR]

There are a few exactly solvable potentials in quantum mechanics for which the completeness relation of the energy eigenstates can be explicitly verified. In this article, we give an elementary proof that the set of bound (discrete) states together with the scattering (continuum) states of the reflectionless potential form a complete set. We also review a direct and elegant derivation of the energy eigenstates with proper normalization by introducing an analog of the creation and annihilation operators of the harmonic oscillator problem. We further show that, in the case of a single bound state, the corresponding wave function can be found from the knowledge of continuum eigenstates of the system. Finally, completeness is shown by using the even/odd parity eigenstates of the Hamiltonian, which provides another explicit demonstration of a fundamental property of quantum mechanical Hamiltonians. Editor's Note: The reflectionless potential, also called the Pöschl–Teller potential, is one of the less-often discussed quantum potentials with known analytical solutions. The system has many interesting properties, including the fact that it allows both bound and scattering states and that the potential well never reflects incident particles. The authors here present new ways to think about the somewhat counter-intuitive completeness of the set of bound and scattering states of the system. [ABSTRACT FROM AUTHOR]

In this study, we analyze a symmetrical anharmonic oscillator that differs from a basic harmonic oscillator by including additional terms in the potential energy function. This oscillator's nonlinear characteristics are important in many physics fields, allowing for modeling of complex systems. We begin by creating the Lagrangian and obtaining the equation of motion through the Euler–Lagrange equation. Both the multi-step differential transforms method (Ms-DTM) and the Runge–Kutta 4th-order (RK4) method are employed to solve this equation, providing both analytical and numerical solutions. By examining these solutions, we confirm our findings and enhance our comprehension of the oscillator's behavior, which can be applied to more intricate nonlinear systems. [ABSTRACT FROM AUTHOR]

In the initial part of this paper, we survey (in arbitrary spacetime dimension) the general FLRW cosmologies with non-interacting perfect fluids and with a canonical or phantom scalar field, minimally coupled to gravity and possibly self-interacting; after integrating the evolution equations for the fluids, any model of this kind can be described as a Lagrangian system with two degrees of freedom, where the Lagrange equations determine the evolution of the scale factor and the scalar field as functions of the cosmic time. We analyze specific solvable models, paying special attention to cases with a phantom scalar; the latter favors the emergence of nonsingular cosmologies in which the Big Bang is replaced, e.g., with a Big Bounce or a periodic behavior. As a first example, we consider the case with dust (i.e., pressureless matter), radiation, and a scalar field with a constant self-interaction potential (this is equivalent to a model with dust, radiation, a free scalar field and a cosmological constant in the Einstein equations). In the phantom subcase (say, with nonpositive spatial curvature), this yields a Big Bounce cosmology, which is a non-absurd alternative to the standard (Λ CDM) Big Bang cosmology; this Big Bounce model is analyzed in detail, even from a quantitative viewpoint. We subsequently consider a class of cosmological models with dust and a phantom scalar, whose self-potential has a special trigonometric form. The Lagrange equations for these models are decoupled passing to suitable coordinates (x , y) , which can be interpreted geometrically as Cartesian coordinates in a Euclidean plane: in this description, the scale factor is a power of the radius r = x 2 + y 2 . Each one of the coordinates x , y evolves like a harmonic repulsor, a harmonic oscillator, or a free particle (depending on the signs of certain constants in the self-interaction potential of the phantom scalar). In particular, in the case of two harmonic oscillators, the curves in the plane described by the point (x , y) as a function of time are the Lissajous curves, well known in other settings but not so popular in cosmology. A general comparison is performed between the contents of the present work and the previous literature on FLRW cosmological models with scalar fields, to the best of our knowledge. [ABSTRACT FROM AUTHOR]

This contribution presents an evaluation of the effectiveness of the low-cost GNSS technique in structural health monitoring and GNSS-seismology applications. To evaluate the ability of the low-cost GNSS technique, harmonic oscillation, and earthquake tests were carried out employing the ZED-F9P-02B OEM low-cost GNSS receiver and two low-cost antennas (A10 and ANN-MB U-Blox) on a single-axis shake table. Harmonic motion experiments include frequencies ranging from 0.35 to 5.80 Hz and amplitudes between 10 and 25 mm. Moreover, the Loma-Prieta and Kobe earthquakes were simulated using a shake table to evaluate the ability of the low-cost GNSS technique to detect earthquake-induced strong ground motions. GNSS observations collected at a 20 Hz sampling interval were processed using the CSRS-PPP online service, and the ability of the low-cost GNSS technique to detect horizontal directional dynamic behaviors was validated using the relative positioning and Linear Variable Differential Transformer (LVDT) data as a reference both time and frequency domain. The max. RMSE values obtained according to the 15 harmonic oscillation test results are 2.8 mm for Geodetic Antenna Relative results, 3.3 mm for PPP, 3.2 mm for A10 Relative, 3.3 mm for PPP, 3.3 mm for UBX Antenna Relative, and 3.7 mm for PPP Results. According to the earthquake test results, the max. RMSE values obtained are 2.6 mm for Geodetic Antenna Relative results, 3.4 mm for PPP, 2.4 mm for A10 Relative, 3.8 mm for A10 PPP, 2.9 mm for UBX Antenna Relative and 4.2 mm for PPP. All results have shown that the ZED-F9P-02B GNSS receiver efficiently detects natural frequencies and structural behaviors. [ABSTRACT FROM AUTHOR]

The use of entropy concepts in the field of stochastic electrodynamics is briefly reviewed here. Entropy calculations that have been fully carried out to date are discussed in two main cases: first, where electric dipole oscillators interact with zero-point, or zero-point plus Planckian, or Rayleigh–Jeans radiation; and second, where only these radiation fields exist within a cavity. The emphasis here is on the first, more complicated, case, where both charged particles and radiation fields are present and interacting. Unlike the usual exposition on entropy in classical statistical mechanics, involving probabilistic notions of phase-space occupation, the calculations to date for both particles and fields, or for fields alone, follow the caloric entropy method, where the notions of heat flow, adiabatic surfaces, and isothermal conditions are utilized. Probability notions certainly still enter into the calculations, as the fields and charged particles interact stochastically together, following Maxwellian electrodynamics. Examples of phase-space calculations for harmonic oscillators and classical hydrogen atoms are carried out, emphasizing how much farther caloric entropy calculations have successfully gone. [ABSTRACT FROM AUTHOR]

In this paper, we present a structured approach to solving the quantum mechanical problem of a particle in 1D periodic square well potential to obtain energy eigenvalues. Here, we utilize the modified Marsiglio's matrix mechanics method to obtain energy eigenvalues for the potential. The method is implemented in a Gnumeric spreadsheet environment, a free open source software that has an in-built eigensolver, to gain clarity regarding each of the steps involved by choosing a smaller-sized H-matrix. The resultant eigenvalues obtained using the simulation are plotted with respect to k values to visualize the band structure diagrams arising from various periodic potentials such as a harmonic oscillator, inverted harmonic oscillator, and linear well potential. This implementation strategy helps us study the physical system in a more systematic and simpler way, pedagogically. [ABSTRACT FROM AUTHOR]

This article presents a vibration signal analysis method to diagnose helicopter turboshaft engine defects such as bearing imbalance and wear. The scientific novelty of the article lies in the development of a comprehensive approach to diagnosing helicopter turboshaft engine defects based on the vibration signals amplitude and frequency characteristics integral analysis combined with a neural network for probabilistic defect detection. Unlike existing methods, the proposed approach uses the energy criterion for the vibration characteristics. It averages the assessment of unique signal processing algorithms, which ensures reliable defect classification under flight vibration conditions. The method is based on representing vibration signals as a sum of harmonic oscillations supplemented by noise components, which helps to identify deviations from typical values. The developed method includes a state function in which the amplitudes and frequency characteristics from nominal parameters estimate deviations. When the critical threshold is exceeded, the function signals possible malfunctions. A multilayer neural network is used to classify defect types, providing high classification accuracy (from 0.985 to 0.994). Computer experiments on the developed seminaturalistic modeling stand confirm that the method can detect increased vibration levels, which is the potential failure indicator. Comparative analysis shows the proposed method's accuracy and noise resistance superiority, emphasizing the importance of introducing modern technologies to improve aircraft operation reliability and safety. [ABSTRACT FROM AUTHOR]

How do transformers model physics? Do transformers model systems with interpretable analytical solutions or do they create an "alien physics" that is difficult for humans to decipher? We have taken a step towards demystifying this larger puzzle by investigating the simple harmonic oscillator (SHO), x ¨ + 2 γ x ˙ + ω 0 2 x = 0 , one of the most fundamental systems in physics. Our goal was to identify the methods transformers use to model the SHO, and to do so we hypothesized and evaluated possible methods by analyzing the encoding of these methods' intermediates. We developed four criteria for the use of a method within the simple test bed of linear regression, where our method was y = w x and our intermediate was w: (1) Can the intermediate be predicted from hidden states? (2) Is the intermediate's encoding quality correlated with the model performance? (3) Can the majority of variance in hidden states be explained by the intermediate? (4) Can we intervene on hidden states to produce predictable outcomes? Armed with these two correlational (1,2), weak causal (3), and strong causal (4) criteria, we determined that transformers use known numerical methods to model the trajectories of the simple harmonic oscillator, specifically, the matrix exponential method. Our analysis framework can conveniently extend to high-dimensional linear systems and nonlinear systems, which we hope will help reveal the "world model" hidden in transformers. [ABSTRACT FROM AUTHOR]

The objectives of NSTX-U research are to reinforce the advantages of STs while addressing the challenges. To extend confinement physics of low- A, high beta plasmas to lower collisionality levels, understanding of the transport mechanisms that set confinement performance and pedestal profiles is being advanced through gyrokinetic simulations, reduced model development, and comparison to NSTX experiment, as well as improved simulation of RF heating. To develop stable non-inductive scenarios needed for steady-state operation, various performance-limiting modes of instability were studied, including MHD, tearing modes, and energetic particle instabilities. Predictive tools were developed, covering disruptions, runaway electrons, equilibrium reconstruction, and control tools. To develop power and particle handling techniques to optimize plasma exhaust in high performance scenarios, innovative lithium-based solutions are being developed to handle the very high heat flux levels that the increased heating power and compact geometry of NSTX-U will produce, and will be seen in future STs. Predictive capabilities accounting for plasma phenomena, like edge harmonic oscillations, ELMs, and blobs, are being tested and improved. In these ways, NSTX-U researchers are advancing the physics understanding of ST plasmas to maximize the benefit that will be gained from further NSTX-U experiments and to increase confidence in projections to future devices. [ABSTRACT FROM AUTHOR]

This study investigates the dynamic behavior and vibration mitigation of a fractional single-degree-of-freedom (SDOF) viscoelastic shape memory alloy spring oscillator system subjected to harmonic external forces. A fractional derivative approach is employed to characterize the viscoelastic properties of shape memory alloy materials, leading to the development of a novel fractional viscoelastic model. The model is then theoretically examined using the averaging method, with its effectiveness being confirmed through numerical simulations. Furthermore, the impact of various parameters on the system's low- and high-amplitude vibrations is explored through a visual response analysis. These findings offer valuable insights for applying fractional sliding mode control (SMC) theory to address the system's vibration control challenges. Despite the high-amplitude vibrations induced by the fractional order, SMC effectively suppresses these vibrations in the shape memory alloy spring system, thereby minimizing the risk of catastrophic events. [ABSTRACT FROM AUTHOR]

Given an autonomous second-order ordinary differential equation (ODE), we define a Riemannian metric on an open subset of the first-order jet bundle. A relationship is established between the solutions of the ODE and the geodesic curves with respect to the defined metric. We introduce the notion of energy foliation for autonomous ODEs and highlight its connection to the classical energy concept. Additionally, we explore the geometry of the leaves of the foliation. Finally, the results are applied to the analysis of Lagrangian mechanical systems. In particular, we provide an autonomous Lagrangian for a damped harmonic oscillator. [ABSTRACT FROM AUTHOR]

This study investigates the generalized Nosé–Hoover system. The original version of the system is a chaotic system designed to represent the interaction between a harmonic oscillator and a heat bath maintained at a constant temperature. Despite its simplicity in just three dimensions, it exhibits complex and unusual dynamics. This investigation focuses on studying local bifurcations, including Saddle-Node and Hopf bifurcations, of the generalized Nosé–Hoover system. In terms of cyclicity, the Lyapunov quantities technique is used to demonstrate that three periodic orbits can bifurcate from the Hopf point. This mathematical research contributes to understanding the equilibrium points, their stability and the dynamics of the nonlinear model when some of the parameters are varied. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate some Morse-type oscillators. In its original form, it is a model for describing the vibrations of a diatomic molecule. The Morse potential generalizes the harmonic oscillator by introducing deviations from the classical theoretical model. In the present study, we perturbed the Morse differential equation by several periodic terms based on the cosine function and by a damping term. The frequency is driven by different coefficients. The size of the deviations is controlled by another constant. We provide two modifications w.r.t. the damping term. The Melnikov approach is applied as an indicator of the possible chaotic opportunities. We also propose a novel approach for stochastic control of the perturbations. It is based on the assumption that the coefficients of the periodic terms are the probabilities of underlying distribution. As a result, the dynamics are driven by its characteristic function. Several applications are considered. We demonstrate some specialized modules for investigating the dynamics of the proposed models, along with the synthesis of radiating antenna patterns. [ABSTRACT FROM AUTHOR]

Quantum deformations offer valuable perspectives into quantum mechanics, particularly by advancing our understanding of symmetry and algebraic structures.The Dunkl oscillator, which integrates Dunkl operators into the harmonic oscillator framework, advances the system's algebraic properties and opens new approaches for exploring quantum phenomena. Supersymmetric quantum mechanics (SSQM) unifies bosonic and fermionic aspects and facilitates the construction of solvable models using generalized Dunkl operators. This paper introduces a new approach to the Dunkl oscillator, employing a complex reflection operator to deepen the understanding of its connection to Hermite polynomials on radial lines. The results offer new perspectives on the Dunkl oscillator's algebraic structure and its relevance to SSQM and quantum deformation theory, expanding the potential for discovering solvable quantum models. [ABSTRACT FROM AUTHOR]

In the autonomous Duffing-Holmes oscillator, the existence of periodic orbits was detected numerically. Using the Hopf bifurcation theory, we prove analytically that such periodic orbits exist. We also provide the exact bifurcation value where the Hopf bifurcation takes place. [ABSTRACT FROM AUTHOR]

Hexamethyldisiloxane (HMDSO) is an organosilicon compound with a modifiable bandgap, depending on the deposition conditions. This material has many unique properties due to its stability, low toxicity, and strong adhesion, making it useful as a protective barrier against corrosion, moisture, and oxidation. In this work, HMDSO films were deposited on glass substrates by the Plasma Enhanced Chemical Vapor Deposition (PECVD) technique at different deposition times. The optical properties of HMDSO films, such as dielectric permittivity, refractive index, extinction and absorption coefficients, and band gap energy, are inferred from transmission and reflection spectra. As the deposition time increased, the real part of the dielectric constant, the refractive index, and the bandgap energy showed a decrease, dropping from 4.24 to 3.40, from 2.06 to 1.84, and from 2.85 eV to 2.03 eV, respectively. The latter result is determined using classical models such as the O'Leary-Johnson-Lim ('OJL') interband transition and the harmonic oscillator model. HMDSO and Silver are used in this study for the fabrication of optical filters using two types of structures, a multiple cavity metal–dielectric (MCMD) and the Fabry–Perot structure. The silver layers are deposited by a sputtering process. The MCMD optical filter shows a higher transmittance of about 30%, but a wide range of wavelengths is transmitted. In contrast, the Fabry–Perot filter showed high contrast but a lower transmittance of about 20%. [ABSTRACT FROM AUTHOR]

Owing to their excellent optoelectronic properties, halide perovskites (HPs) have garnered significant attention in the field of optoelectronics. However, conventional HPs‐based optoelectronic devices primarily are fabricated using solution‐based processes, implying that extremely time‐consuming needs to individually synthesize their composition‐dependent optoelectronic properties. This study demonstrates the feasibility of combining first‐principles simulations with combinatorial synthesis, comparing the effects of HP properties on optoelectronic devices using this combined approach. The first‐principles simulations confirm that increasing the ratio of small halide ions increased the band gap by k·p perturbation theory and harmonic oscillator models. By fabricating HP thin films with compositional gradients using combinatorial synthesis, it is confirmed that an increase in band gap corresponds to a decrease in static relative permittivity. Furthermore, HP‐based optoelectronic devices are fabricated to measure their photoelectric conversion efficiency and responsivity based on the simulated and measured relative permittivity, including time‐resolved photoluminescence. The findings demonstrate the influence of the relative permittivity on device performance, elucidating the relationship between band structure and relative permittivity. Therefore, in this study, the potential of combining first‐principles simulations with combinatorial synthesis is confirmed by comparing the relative permittivity characteristics of optoelectronics developed using this combined approach. [ABSTRACT FROM AUTHOR]

IoT sensors are crucial for visualizing multidimensional and multimodal information and enabling future IT applications/services such as cyber-physical spaces, digital twins, autonomous driving, smart cities and virtual/augmented reality (VR or AR). However, IoT sensors need to be battery-free to realistically manage and maintain the growing number of available sensing devices. Here, we provide a novel sensor design approach that employs metasurfaces to enable multifunctional sensing without requiring an external power source. Importantly, unlike existing metasurface-based sensors, our metasurfaces can sense multiple physical parameters even at a fixed frequency by breaking classic harmonic oscillations in the time domain, making the proposed sensors viable for usage with limited frequency resources. Moreover, we provide a method for predicting physical parameters via the machine learning-based approach of random forest regression. The sensing performance was confirmed by estimating the temperature and light intensity, and excellent determination coefficients larger than 0.96 were achieved. Our study affords new opportunities for sensing multiple physical properties without relying on an external power source or requiring multiple frequencies, which markedly simplifies and facilitates the design of next-generation wireless communication systems. Metasurface-based sensors provide a battery-free sensing solution for maintaining numerous IoT devices with little human resources. However, the conventional method exploited resonant mechanisms associated with multiple physical parameters through different frequencies, although available frequencies were strictly limited. We report the first sensor design approach using circuit-based metasurfaces that offer a higher degree of freedom to design time-varying scattering profiles associated with multiple physical properties at a single frequency. Our prototype detects light intensity and temperature with an excellent determination coefficient above 0.96 via a machine-learning technique. [ABSTRACT FROM AUTHOR]

The increasing penetration of power electronics, such as grid-connected inverters and active loads may cause power quality issues, which reduce the sensitivity of monitoring and control systems due to measurement noises. This article presents an optimal singular value decomposition (SVD) filtering method for grid-connected inverters to improve sampling accuracy against measurement noises. First, the principle of this proposed method is based on the Hankel matrix theory, and then the implementation process is explained, during which the relationship between the Hankel matrix dimension and noise reduction is discussed. Furthermore, the optimal singular value is analyzed and proposed to determine the reconstruction order. Then, the comparative analysis of the proposed optimal SVD filtering method and difference spectrum method is given to explain the optimal reconstruction order. Finally, simulation verifications are implemented to validate the effectiveness of the proposed filtering method, considering the Hankel matrix dimension, reconstruction order, and different signal–noise ratio (SNR). The verification results show that the proposed optimal SVD filtering method can accurately identify the sampling current of grid-connected inverters, even if severe harmonic noises and oscillation happen. The proposed method can reduce the effects of harmonic disturbance on measurement accuracy and control performance of grid-connected inverters, which can improve the robustness of grid-connected inverters. [ABSTRACT FROM AUTHOR]

Narrowband terahertz (THz) detection plays a key role in biomedical imaging, biological applications, and security screening. Particularly rapid resolution of material differences based on spectral fingerprints or time‐resolved observation of the materials conformational state typically requires only the measurement of spectral information at a few selected frequencies. Here, a high‐performance resonance‐based coupled photoconductive antenna (PCA) was designed, which consists of a square split‐ring resonator (SRR) and an H‐shaped antenna. The incident THz wave energy can be effectively coupled in the gap of the H‐shaped antenna, and the coupling effect base on coupled harmonic oscillator model can be effectively strengthened. By decreasing the square SRR gap width HD, the relative position parameters of d and L3 between the square SRR and H‐shaped antenna can markedly improve the resonance frequency sensitivity with inductive–capacitive resonance. With the square SRR arm length L1 = L2 = L increased, the resonance frequency markedly shifted toward a lower frequency and the resonance sensitivity increased. The results prove that the THz frequency selection detection range of the coupled PCA can be designed to 0.1∼1.0 THz. Compared with the traditional H‐shaped photoconductive detection antenna, the detection resonance peak shifted the lower frequency and the maximum THz detection sensitivity increased by approximately two orders of magnitude at 0.2528 THz. The structure of the noncontact micrometer–coupled PCA is simple and easy to fabricate and integrate. Our findings may also help to advance the use of THz technology in rapid distinguish material properties. [ABSTRACT FROM AUTHOR]

This manuscript presents a comprehensive exploration of the nonlinear charged particle oscillation equation, employing the Laplace–Adomian decomposition method (LDM) to obtain approximate analytical solutions. The investigation leads to the formulation of five initial equations governing the oscillatory behavior of a charged particle, which are visually represented and analyzed with insightful interpretations. Notably, the existing literature lacks an exact solution to this problem. However, this paper fills this gap by presenting an approximate analytical solution utilizing the LDM. The solution is carefully studied and analyzed, contributing to a deeper understanding of the complex behavior of charged particle oscillation. [ABSTRACT FROM AUTHOR]

Through the implementation of a streaming filter, output of numerical ocean simulations can be band‐pass filtered at tidal frequencies while the model is running, yielding time series of sinusoidal motions consisting of tidal signals in the filter's target frequency band. The filtering algorithm is developed from a system of two ordinary differential equations that represents the motion of a damped harmonic oscillator. The filter's response to a broadband input signal is unity at its target frequency but vanishes toward the low and high frequency limits. The decay of the filter response is controlled by a dimensionless parameter, which determines the filter's bandwidth. As a result, the filter allows signals within a small frequency band around its target frequency to pass through, while blocking signals outside of its target frequency band. In this work, the filtering algorithm is implemented into the barotropic solver of the Modular Ocean Model version 6 (MOM6) for determining the instantaneous tidal velocities of the semi‐diurnal and diurnal tides. Utilizing the filters, the frequency‐dependent internal wave drag is applied to the semi‐diurnal and diurnal frequency bands separately. The simulation results suggest that the performance of the algorithm is consistent with the filter transfer function in Fourier space. Potential applications of the algorithm also include de‐tiding the model output for nested regional ocean models, especially those for the purpose of operational forecasting. Plain Language Summary: In this work, we developed a computationally efficient algorithm for detecting tidal signals from the instantaneous model output, without needing to harmonically analyze the entire time series of model output. This is achieved through the construction of a streaming filter, which takes the instantaneous model output as the input and returns a time series consisting of tidal motions at its target frequency band as the output, in a process that effectively allows signals within its target frequency band to pass through and blocks signals outside of its target frequency band. Unlike the conventional harmonic analysis, the band‐pass filtering process does not require information from any of the previous or future time steps. The filtering algorithm is implemented and validated in a global ocean model. The filters can be utilized to parameterize frequency‐dependent internal wave drag, as demonstrated in this work, and to remove tidal signals from the model output, which has potential application in regional ocean forecasting systems. Key Points: The streaming band‐pass filter can detect sinusoidal motions at tidal frequencies from the instantaneous model outputThe filtering algorithm is computationally efficient and is capable of capturing the temporal variation of tidal signalsThe filters can be utilized to parameterize frequency‐dependent internal wave drag and to de‐tide model output [ABSTRACT FROM AUTHOR]

In this paper, we explore the ground state energy of an anharmonic oscillator and its special cases, such as the harmonic oscillator and particle in the box, applying generalized uncertainty relations in quantized space with minimal length. Consequently, we introduce a novel approach for estimating the ground state energy of quantum systems in deformed space. By using only the Hamiltonian of the system and generalized uncertainty relations, we manage to calculate a conditional extremum which corresponds to the minimal energy of the system, as allowed by the minimal length model. For a harmonic oscillator in deformed space with minimal length, the lower boundary estimation for the ground state energy corresponds to the exact value found by solving the Schrodinger equation. In the case of an anharmonic oscillator with an arbitrary parameter n, we manage to find an exact solution through a linear approximation with respect to the deformational parameter, considering it a small quantity. In our case, n represents the degree of the coordinate in the anharmonic oscillator Hamiltonian. When we set n = 1 in our solution for the anharmonic oscillator, it can be found that it corresponds to the harmonic oscillator solution through a linear approximation based on the deformational parameter, as expected. When n→∞, we derive an expression that corresponds to the lower boundary estimation of the ground state energy of a particle in a box, which we compare with the exact solution. Our estimation fell below the exact solution found by solving the Schrodinger equation, which is a common occurrence in estimation methods. Considering the advantages offered by our method for estimating ground state energies in deformed spaces with minimal length, including its simplicity of application and the satisfactory accuracy of results, this approach can effectively extend to determining the ground state energies of various other systems. [ABSTRACT FROM AUTHOR]

We present a hyperchaotic oscillator with two linear terms and seven nonlinear terms that displays special algebraic properties. Notably, the introduced oscillator features distinct equilibrium types: single-point, line, and spherical equilibria. The introduced oscillator exhibits attractive dynamics like hyperchaos with two wing attractors. To gain a better understanding, we provide the bifurcation and Lyapunov exponents. The Kolmogorov–Sinai entropy is applied to show the complexity of the oscillator. A microcontroller realization confirms the reliability of the oscillator. The proposed oscillator is successfully applied for RNG. [ABSTRACT FROM AUTHOR]

There are several versions of the damped form of the celebrated Pinney equation, which is the natural partner of the undamped time-dependent harmonic oscillator. In this work, these dissipative versions of the Pinney equation are briefly reviewed. We show that Noether's theorem for the usual time-dependent harmonic oscillator as a guiding principle for derivation of the Pinney equation also works in the damped case, selecting a Noether symmetry-based damped Pinney equation. The results are extended to general nonlinear damped Ermakov systems. A certain time-rescaling always allows to remove the damping from the final equations. [ABSTRACT FROM AUTHOR]

In this paper, we construct a smooth vector bundle over the deformation to the normal cone DNC(V,M) through a rescaling of a vector bundle E → V, which generalizes the construction of the spinor rescaled bundle over the tangent groupoid by Nigel Higson and Zelin Yi. We also provide an equivariant version of their construction. As the main application, we recover the Kirillov character formula for the equivariant index of Dirac-type operators. As another application, we get an equivariant generalization of the description of the Witten and the Novikov deformations of the de Rham-Dirac operator using the deformation to the normal cone obtained recently by O. Mohsen. [ABSTRACT FROM AUTHOR]

The method of quantum dynamics is employed to investigate the mean strategy in the swarm intelligence algorithm. The physical significance of the population mean point is explained as the location where the optimal solution with the highest likelihood can be found once a quantum system has reached a ground state. Through the use of the double well function and the CEC2013 test suite, controlled experiments are conducted to perform a comprehensive performance analysis of the mean strategy. The empirical results indicate that implementing the mean strategy not only enhances solution diversity but also yields accurate, efficient, stable, and effective outcomes for finding the optimal solution. [ABSTRACT FROM AUTHOR]

In this paper, we examine the role of the Jacobi last multiplier in the context of two-dimensional oscillators. We first consider two-dimensional unit-mass oscillators admitting a separable Hamiltonian description, i.e., H = H 1 + H 2 , where H 1 and H 2 are the Hamiltonians of two one-dimensional unit-mass oscillators. It is shown that there exists a third functionally-independent first integral Θ , ensuring superintegrability. Various examples are explicitly worked out. We then consider position-dependent-mass oscillators and the Bateman pair, where the latter consists of a pair of dissipative linear oscillators. Quite remarkably, the Bateman pair is found to be superintegrable, despite admitting a Hamiltonian which cannot be separated into two isolated (non-interacting) one-dimensional oscillators. [ABSTRACT FROM AUTHOR]

This document provides a historical overview of the development of the concept of intrinsic angular momentum, or "spin," of the photon. It discusses the contributions of Bose and Einstein in postulating the spin of the photon and the quantization of energy, momentum, and angular momentum in particles and atoms. The document also explores the understanding of field energy and momentum in physics, including the arguments made by Maxwell, Thomson, and Heaviside. It further discusses the electromagnetic momentum density and the transfer of field angular momentum to mechanical angular momentum. Additionally, the document mentions the Feynman disk paradox and the quantization of angular momentum. [Extracted from the article]

Ultrafast optical spectroscopy is an effective experimental technique for accessing electronic and atomic motions in materials at their fundamental timescales and studying their responses to external perturbations. Despite the important insights that ultrafast techniques can provide on the microscopic physics of solids, undergraduate students' exposure to this area of research is still limited. In this article, we describe an ultrafast optical pump-probe spectroscopy experiment for the advanced undergraduate instructional laboratory, in which students can measure coherently excited vibrations of the crystal lattice and connect their observations to the microscopic properties of the investigated materials. We designed a simple table-top apparatus based on a commercial Er-fiber oscillator emitting 50-fs pulses at 1560 nm and at 100 MHz repetition rate. We split the output into two beams, using one of them as an intense "pump" to coherently excite phonons in selected crystals, and the other as a weaker, delayed "probe" to measure the transient reflectivity changes induced by the pump. We characterize the ultrafast laser pulses via intensity autocorrelation measurements and detect coherent phonon oscillations in the reflectivity of Bi, Sb, and 1T-TaS2. We then discuss the oscillation amplitude, frequency, and damping in terms of microscopic properties of these systems. Editor's Note: This paper provides an introduction to modern time-domain spectroscopy using ultrafast lasers, an experimental technique used to observe fundamentally important phenomena in condensed matter physics as well as in other fields. As a specific example, the authors demonstrate the generation and detection of coherent phonons in three solids. The paper provides an undergraduate-accessible discussion of the theory of coherent phonon spectroscopy in terms of classical harmonic oscillator physics. Then, a relatively low-cost ultrafast pump-probe spectroscopy system and the experimental procedures that the authors use in their experiment are described. Finally, typical experimental data and analysis methods are presented. This laboratory experiment is a welcome addition to the undergraduate physics curriculum, introducing a system that is suitable for examining a variety of ultrafast and nonequilibrium phenomena in an advanced instructional laboratory. [ABSTRACT FROM AUTHOR]

In this article, we compute the Feynman propagator for a simple harmonic oscillator coupled to a constant electric field using Schwinger's method, which is based on the solution of the Heisenberg equations for the position and canonical momentum operators. Such solutions are then used to write the ordered Hamiltonian operator of the position operators ... (O) and ... (t). The utilization of proper operator ordering, along with subsidiary and initial conditions, results in the yield of such a propagator. We found that the propagator obtained is consistent with the one obtained using the Feynman path integral in the work of Poon and Muñoz (Poon & Muñoz 1999). We anticipate that this technique will be advantageous and widely recognized for physics students. [ABSTRACT FROM AUTHOR]

An important application of the Hermite polynomials with the weight function absorbed into them is that they form the solutions of the differential equation for a simple harmonic oscillator. Motivated by this fact, our focus for this work is to investigate a class of singular integral equations whose kernels are formed by the generating function for the Hermite polynomials with the weighting function absorbed into them. We propose an efficient method for solving such a class of singular integral equations. In addition, we establish the results of applications involving the integral of Hermite polynomials and their generating functions. [ABSTRACT FROM AUTHOR]

We study solutions of the collisionless Boltzmann equation (CBE) in a functional Koopman representation. This facilitates the use of linear spectral techniques characteristic of the analysis of Schrödinger-type equations. For illustrative purposes, we consider the classical phase mixing of a non-interacting distribution function in a quartic potential. Solutions are determined perturbatively relative to a harmonic oscillator. We impose a form of coarse-graining by choosing a finite-dimensional basis to represent the distribution function and time evolution operators, which sets a minimum length-scale on phase space structure. We observe a relationship between the dimension of the representation and the multiplicity of the harmonic oscillator eigenvalues. System dynamics are understood in terms of degenerate subspaces of the linear operator spectra. Each subspace is associated with a mode of the harmonic oscillator, the first two being bending and breathing structures. The quartic potential splits the degenerate eigenvalues within each subspace. This facilitates the formation of spiral structure as deformations from the harmonic oscillator modes. We ultimately argue that this construction provides a promising avenue for study of self-interacting systems experiencing phase mixing, which is an outstanding problem in the context of the Gaia DR2 vertical phase space spirals. [ABSTRACT FROM AUTHOR]

Cracks, common indicators of deterioration in bridge frameworks, frequently stem from wear and rust, leading to increased local flexibility and changes in the structure's dynamic behavior. This study examines how these cracks affect the dynamics of footbridges when subjected to loads generated by walking individuals. The pedestrian is modeled as a linear oscillator, while the cracked bridge is represented by a simply supported beam following Euler–Bernoulli's theory. The use of the Dirac delta function allows for the precise representation of the localized stiffness reduction at the crack location, facilitating the calculation of analytical expressions for the beam's vibration modes. The research suggests that the presence of cracks minimally affects the bridge's mid-span displacement. However, with a limited depth of cracks, the appearance of cracks notably amplifies the mid-span acceleration amplitude of the bridge, leading to a pronounced concentration of energy at the third natural frequency of the bridge in the acceleration spectrum. As the depth and number of cracks increase, the acceleration amplitude continues to decrease, but the corresponding spectrum remains almost unchanged. The study's outcomes enhance the comprehension of how cracks affect the performance of bridge structures when subjected to loads from pedestrians, offering insights for the monitoring and evaluation of the condition of cracked footbridges. [ABSTRACT FROM AUTHOR]

We introduce a new framework for the nuclear structure calculations, which describes the single-particle wave function as a superposition of localized Gaussians. It is a hybrid of the Hartree–Fock and antisymmetrized molecular dynamics (AMD) models. In the numerical calculations of oxygen, calcium isotopes, and |$^{100}{\rm Sn}$|⁠ , the framework shows its potential by significantly improving upon AMD and yielding results that are consistent with or even better than Hartree–Fock(–Bogoliubov) calculations based on harmonic oscillator expansions. In addition to the basic equations, general forms of the matrix elements are also given. [ABSTRACT FROM AUTHOR]

Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadrature-based models according to the integral form of the SHSs' solutions, where we denoise the loss-by-moment calculations of the solutions. The integral pattern of the models transforms the source of the essential learning error from the discrepancy between the modified Hamiltonian and the true Hamiltonian in the classical HNN models into that between the integrals and their quadrature approximations. This transforms the challenging task of deriving the relation between the modified and the true Hamiltonians from the (stochastic) Hamilton–Jacobi PDEs, into the one that only requires invoking results from the numerical quadrature theory. Meanwhile, denoising via moments calculations gives a simpler data fitting method than, e.g., via probability density fitting, which may imply better generalization ability in certain circumstances. Numerical experiments validate the proposed learning strategy on several concrete Hamiltonian systems. The experimental results show that both the learned Hamiltonian function and the predicted solution of our quadrature-based model are more accurate than that of the corrected symplectic HNN method on a harmonic oscillator, and the three-point Gaussian quadrature-based model produces higher accuracy in long-time prediction than the Kramers–Moyal method and the numerics-informed likelihood method on the stochastic Kubo oscillator as well as other two stochastic systems with non-polynomial Hamiltonian functions. Moreover, the Hamiltonian learning error ε H arising from the Gaussian quadrature-based model is lower than that from Simpson's quadrature-based model. These demonstrate the superiority of our approach in learning accuracy and long-time prediction ability compared to certain existing methods and exhibit its potential to improve learning accuracy via applying precise quadrature formulae. [ABSTRACT FROM AUTHOR]