Harmonic Oscillator Research Articles

Spectroscopic properties under vibrational strong coupling in disordered matter from path-integral Monte Carlo simulations

Vibrational strong coupling (VSC), the strong coupling between a Fabry–Perrot cavity and molecular vibrations at mid-infrared frequencies, has received important attention in the last years due to its capacity of modifying both vibrational spectra and chemical reactivity. VSC is a collective effect, and in this work, we introduce Path Integral Monte Carlo (PIMC) simulations that not only take into account the quantum character of the molecular vibrations and of the optical resonance of the cavity but also reproduce this collective behavior by considering multiple replicas of the molecular system. Moreover, we show that it is possible to extract from the PIMC simulations the decomposition of the hybrid optical and molecular states in terms of the bare molecular modes. On a model system of an ensemble of disordered Morse oscillators coupled to a single cavity through the Pauli–Fierz Hamiltonian, PIMC can retrieve known features obtained from analytical modes such as the Tavis–Cummings model and obtain a very close agreement with exact diagonalization for a small number of Morse oscillators. We also find that notwithstanding the anhamonic character of the Morse oscillators, the collective mode coupled to the cavity behaves as a harmonic oscillator, following the quantum central limit theorem.

The hydrogen atom perturbed by a 1-dimensional Simple Harmonic Oscillator (1d-SHO) potential

Abstract The hydrogen atom perturbed by a constant 1-dimensional weak quadratic potential λz2 is solved at first-order perturbation theory using the eigenstates of the total angular momentum operator - the coupled basis. Physical applications of this result could be found, for example, in the study of a quadratic Zeeman effect weaker than fine-structure effects, or in a perturbation caused by instantaneous generalised van der Waals interactions.

On the two-dimensional harmonic oscillator with an electric field confined to a circular box

Abstract We revisit the quantum-mechanical two-dimensional harmonic oscillator with an electric field confined to a circular box of impenetrable walls. In order to obtain the energy spectrum we resort to the Rayleigh-Ritz method with polynomial and Gaussian basis sets. We compare present results with those derived recently by other authors. We discuss the limits of large and small box radius and also do some calculations with perturbation theory.

Effects of conical singularity and Wu-Yang magnetic monopole on thermodynamic properties of harmonic oscillator interacting with potential

Abstract This paper investigates the thermodynamic properties of the harmonic oscillator system in a conical singularities background. Moreover, we incorporate a Wu-Yang magnetic monopole (WYMM) and inverse square potential into the quantum system and analyze the resulting effects. Using analytical methods, we derive the energy eigenvalues and study the thermodynamic properties, such as the partition function, Helmholtz free energy, Gibbs's free energy and specific heat capacity at finite temperature $T \neq 0$. Our findings demonstrate that these physical parameters are influenced by the topological parameter, strength of WYMM and potential parameters. These results provide valuable insights into the interplay between thermodynamic properties of a quantum mechanical problem and the gravitational effects.

Similarity among quantum-mechanical states: Analysis and applications for central potentials

Abstract The similarity of quantum-mechanical solutions for central potentials is analytically determined and numerically explored for arbitrary dimensionalities. The study here provided focuses on hydrogenic systems and the harmonic oscillator, in respective non-relativistic frameworks. A diversity of analytical expressions for the Quantum Similarity Measure (QSM) and Index (QSI) are provided. Relevant conclusions are derived from the analyses grounded on state quantum numbers, space dimensionality and on the role played by the main characteristic parameters of these systems, namely the nuclear charge in the hydrogenic case, and the angular frequency for the oscillator. For this purpose, a statistical analysis of the QSI values has been performed for a large number both of states and combinations of them in each system. Considering the factorization of QSI into a radial and an angular part, particular attention is paid to the individual contribution of each part in both systems.

Effects of nanodiamonds on the mechanical properties, acoustic properties, vibration damping, and flame retardancy of ramie-fiber epoxy composite panels used for indoor applications

This research aims to systematically analyze the impact of nanodiamonds (NDs) in ramie fiber-reinforced epoxy resin acoustic panels used for indoor applications. The panels (four variants) are fabricated using six layers of ramie fiber with various weight percentages of NDs (0.0, 0.2, 0.4, and 0.6) in epoxy resin by the vacuum resin infusion process (VRIP). Mechanical characterization (tensile and flexural strength) was carried out using Instron 8801 universal testing machine. The impedance tube-based sound absorption coefficient (SAC) test was performed at low frequency and higher frequency, respectively. The void content in the panel is evaluated using a micro-x-ray computed tomography (CT) scanner. The dispersion of nanoparticles is studied using scanning electron microscopy (SEM) images. The vertical flame-retardant test and the horizontal flame-retardant test were conducted according to the UL-94 standard. The 0.4 wt.% NDs sample showed good tensile strength (59.178 MPa) and flexural strength (69.134 MPa) compared with other panels. The panels showed differences in SAC values for different weight percentages of NDs, both at lower and higher frequencies. The 0.6 wt.% NDs sample attained the maximum SAC of 0.906 at 6000 Hz in the high-frequency and 0.34 at 1112 Hz in the low-frequency. The SEM reveals an even distribution of NDs in both the 0.2 and 0.4 wt.% NDs panels, while agglomerates form in the 0.6 wt.% panels. The CT scan result shows void content both internally and externally in the panels. There are no voids in the panels where NDs are uniformly distributed. The synergistic effect of NDs in epoxy resin forms a char over the burnt surfaces of samples, enhancing the flame-retardant properties of the panels. According to this study, adding NDs to ramie fiber epoxy composites has improved the panels’ necessary qualities, making them suitable for use as indoor acoustic conditioning materials.

Supersymmetric Quesne-Dunkl Quantum Mechanics on Radial Lines

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.

Two-dimensional simulation of generalized thermoelastic damping in vibrations of strain gradient beam resonators

Two-dimensional simulation of generalized thermoelastic damping in vibrations of strain gradient beam resonators

Quantum instability and Ehrenfest time for an inverted harmonic oscillator

We use out-of-time order correlators (OTOCs) to investigate the quantum instability and Ehrenfest time for an inverted harmonic oscillator (IHO). For initial states located in the stable manifolds of the IHO we find that the corresponding OTOC exhibits identical evolutionary characteristics to the saddle point before the Ehrenfest time. For initial states located in the unstable manifolds, the OTOCs still grow exponentially but the time to maintain exponential growth is related to the center position of its wave packet in phase space. Moreover, we use the Husimi Q function to visualize the quantum wave packets during exponential growth of the OTOCs. Our results show that quantum instability exists at arbitrary orbits in the IHO system, and the Ehrenfest time in the IHO system depends not only on the photon number of the initial system but also on the central positions of the initial states in phase space.

Motional-state analysis of a trapped ion by ultranarrowband composite pulses

In this work, we present a method for measuring the motional state of a two-level system coupled to a harmonic oscillator. Our technique uses ultranarrowband composite pulses on the blue sideband transition to scan through the populations of the different motional states. Our approach does not assume any previous knowledge of the motional state distribution and is easily implemented. It is applicable both inside and outside of the Lamb-Dicke regime. For higher phonon numbers especially, the composite pulse sequence can be used as a filter for measuring phonon number ranges. We demonstrate this measurement technique using a single trapped ion and show good detection results with the numerically evaluated pulse sequence. Published by the American Physical Society 2024

Enhancing Eyringpy: Accurate Rate Constants with Canonical Variational Transition State Theory and the Hindered Rotor Model.

The recrossing effect and hindered rotations can lead to significant inaccuracies in rate constant calculations using transition state theory and the harmonic oscillator approximation. To address these issues, we enhanced Eyringpy, a Python-based computational tool, by integrating the canonical variational transition state theory (CVT) and the hindered rotor model, effectively mitigating the limitations of traditional methods. CVT rate constants are calculated using electronic structure data from nonstationary points along the minimum-energy path. Additionally, we developed an algorithm based on reaction force analysis to autonomously select relevant nonstationary points. Torsions are modeled using one-dimensional hindered rotor approaches proposed by Pitzer-Gwinn and Ayala-Schlegel.

An Experimental Study on Vortex-Induced Vibration Suppression of a Long Flexible Catenary Cable by Using Vibration Dampers

In this paper, an experimental study is conducted to investigate the effectiveness of vibration dampers in suppressing vortex-induced vibration in a long, flexible catenary cable with a low mass ratio. The dampers, consisting of two small, symmetric, lightweight pipes clamped to the cable, are sparsely deployed along the cable to shape the vibration characteristics. The experimental results demonstrate that dampers significantly reduce the vibration amplitude by up to 60% and axial tension by up to 61% at high flow velocities, effectively suppressing the cable vibration in perpendicular flow. In addition, it is observed that the in-line and cross-flow vibration frequencies are approximately equal when the dampers are applied. This behavior contrasts with the conventional undamped catenary cable, where the in-line vibration frequencies are double those of the cross-flow frequencies.

Experimental Verification of a Compressor Drive Simulation Model to Minimize Dangerous Vibrations

The article highlights the importance of analytical computational models of torsionally oscillating systems and their simulation for estimating the lowest resonance frequencies. It also identifies the pitfalls of the application of these models in terms of the accuracy of their outputs. The aim of the paper is to control the dangerous vibration of a mechanical system actuator using a pneumatic elastic coupling using different approaches such as analytical calculations, experimental measurement results, and simulation models. Based on the known mechanical properties of the laboratory system, its dynamic model in the form of a twelve-mass chain torsionally oscillating mechanical system is developed. Subsequently, the model is reduced to a two-mass system using the method of partial frequencies according to Rivin. The total load torque of the piston compressor under fault-free and fault conditions is simulated to obtain the amplitudes and phases of the harmonic components of the dynamic torque. After calculating the natural frequency and the natural shape of the oscillation, the Campbell diagram is processed to determine the critical revolutions. There is a pneumatic flexible coupling between the rotating masses, which changes the dynamic torsional stiffness. The dynamic torque curves transmitted by the coupling are compared with different dynamic torsional stiffnesses during steady-state operation and one cylinder failure. The monitored values are the position of the critical revolutions, the natural frequency, the natural shape of the oscillation, and the RMS of the dynamic load torque. The experimental model is verified by the simulation model. The accuracy of the developed simulation model with the experimental data are apparently very good (even more than 99% of the critical revolutions value obtained by calculation); however, it depends on the dynamic stiffness of the coupling. In this study, a detailed, comprehensive approach combining analytical procedures with simulation models is presented. Experimental data are verified with simulation results, which show a good agreement in the case of 700 kPa coupling pressure. The inaccuracy of some of the experiments (at 300 and 500 kPa pressures) is due to the interaction of the coupling’s apparent stiffness and the level of the damped vibration energy in the coupling, which is manifested by its different heating. Based on further experiments, a solution to these problems will be proposed by introducing this phenomenon effectively into the simulation model.

Thermodynamic linear algebra

AbstractLinear algebra is central to many algorithms in engineering, science, and machine learning; hence, accelerating it would have tremendous economic impact. Quantum computing has been proposed for this purpose, although the resource requirements are far beyond current technological capabilities. We consider an alternative physics-based computing paradigm based on classical thermodynamics, to provide a near-term approach to accelerating linear algebra. At first sight, thermodynamics and linear algebra seem to be unrelated fields. Here, we connect solving linear algebra problems to sampling from the thermodynamic equilibrium distribution of a system of coupled harmonic oscillators. We present simple thermodynamic algorithms for solving linear systems of equations, computing matrix inverses, and computing matrix determinants. Under reasonable assumptions, we rigorously establish asymptotic speedups for our algorithms, relative to digital methods, that scale linearly in matrix dimension. Our algorithms exploit thermodynamic principles like ergodicity, entropy, and equilibration, highlighting the deep connection between these two seemingly distinct fields, and opening up algebraic applications for thermodynamic computers.

Experimental Investigation of Tensile, Shear, and Compression Behavior of Additional Plate Damping Structures with Entangled Metallic Wire Material

To fulfill the vibration damping requirements of plate structures under complex conditions, additional damping structures with entangled metallic wire material (EMWM) are proposed based on the excellent physical properties of EMWM. A batch of specimens with different filament diameters, densities, and thicknesses are prepared. The stiffness and loss factors are taken as the evaluation indexes, and orthogonal tests are conducted to obtain the tensile, shear, and compression properties. The results show that the optimal parameter combinations can be obtained through orthogonal tests. For the specimens with optimal parameter combinations, the mechanical tests under different loading rates and loading displacements are carried out. With the increase in loading rate, the tensile and shear forces appear to display fracture failure in advance, and the compression performance is stable without significant changes. The change rule under each mechanical test is explored using the stiffness and loss factor evaluation index. It provides a reference for the analysis of the preparation parameters of subsequent additional damping structures with EMWM.

Comparative analysis of RNN versus IIR digital filtering to optimize resilience to dynamic perturbations in pH sensing for vertical farming

AbstractVertical farming (VF) refers to systems of agriculture where crops are grown in trays stacked vertically by exposing them to artificial light and using sensing technology to improve product quality and yield. In this work, we propose an advanced filtering scheme based on recurrent neural networks (RNNs) and deep learning to enable efficient control strategies for VF applications. We demonstrate that the best RNN model incorporates five neuron layers, with the first and second containing 90 long short‐term memory neurons. The third layer implements one gated recurrent units neuron. The fourth segment incorporates one RNN network, while the output layer is designed by using a single neuron exhibiting a rectified linear activation function. By utilizing this RNN digital filter, we introduce two variations: (1) a scaled RNN model to tune the filter to the signal of interest, and (2) a moving average filter to eliminate harmonic oscillations of the output waveforms. The RNN models are contrasted with conventional digital Butterworth, Chebyshev I, Chebyshev II, and elliptic infinite impulse response (IIR) configurations. The RNN digital filtering schemes avoid introducing unwanted oscillations, which makes them more suitable for VF than their IIR counterparts. Finally, by utilizing the advanced features of scaling of the RNN model, we demonstrate that the RNN digital filter can be pH selective, as opposed to conventional IIR filters.

Optimization of Dynamic Characteristics of Rubber-Based SMA Composite Dampers Using Multi-Body Dynamics and Response Surface Methodology

The suspension system of a commercial vehicle cab plays a crucial role in enhancing ride comfort by mitigating vibrations. However, conventional rubber suspension systems have relatively fixed stiffness and damping properties, rendering them inflexible to load variations and resulting in suboptimal ride comfort under extreme road conditions. Shape memory alloys (SMAs) represent an innovative class of intelligent materials characterized by superelasticity, shape memory effects, and high damping properties. Recent advancements in materials science and engineering technology have focused on rubber-based SMA composite dampers due to their adjustable stiffness and damping through temperature or strain rate. This paper investigates how various structural parameters affect the stiffness and damping characteristics of sleeve-type rubber-based SMA composite vibration dampers. We developed a six-degree-of-freedom vibration differential equation and an Adams multi-body dynamics model for the rubber-based SMA suspension system in commercial vehicle cabins. We validated the model’s reliability through theoretical analysis and simulation comparisons. To achieve a 45% increase in stiffness and a 64.5% increase in damping, we optimized the suspension system’s z-axis stiffness and damping parameters under different operating conditions. This optimization aimed to minimize the z-axis vibration acceleration at the driver’s seat. We employed response surface methodology to design the composite shock absorber structure and then conducted a comparative analysis of the vibration reduction performance of the optimized front and rear suspension systems. This study provides significant theoretical foundations and practical guidelines for enhancing the performance of commercial vehicle cab suspension systems.

The role of structural and insulating material in the structure-borne noise propagation of superyachts

The insulation and noise and vibration damping characteristics of complex systems used by humans, such as automobiles, airplanes and ships are becoming increasingly important from the early design stages to ensure an adequate level of comfort. Especially in the naval fields, the design of insulation plans is crucial to prevent the propagation of noise and vibrations on board of megayachts. Since it is quite complex to identify and correctly model the sources due to their deterministic and random nature, during the early design stage, the focus is on insulation rather than reducing the acoustic levels of the sources themselves. In this article, a method for analyzing sea trials on a superyacht will be proposed with the aim of analyzing how much the insulation materials can limit the levels of vibrational energy on board during the path between sources and receivers. A new a descriptor based on harmonic transmission energy through the structure is proposed for path insertion loss experimental identification. In particular, by using spectral analyses and synchronous averaging of sound levels in various areas of the superyacht, it will be possible to study the vibroacoustic insulation of structural materials and their damping coefficient.

Serum iron and transferrin saturation variation are circadian regulated and linked to the harmonic circadian oscillations of erythropoiesis and hepatic Tfrc expression in mice.

Serum iron has long been thought to exhibit diurnal variation and is subsequently considered an unreliable biomarker of systemic iron status. Circadian regulation (endogenous ~24-h periodic oscillation of a biologic function) governs many critical physiologic processes. It is unknown whether serum iron levels are regulated by circadian machinery; likewise, the circadian nature of key players of iron homeostasis is unstudied. Here we show that serum iron, transferrin saturation (TSAT), hepatic transferrin receptor (TFR1) gene (Tfrc) expression, and erythropoietic activity exhibit circadian rhythms. Daily oscillations of serum iron, TSAT, hepatic Tfrc expression, and erythropoietic activity are maintained in mice housed in constant darkness, where oscillation reflects an endogenous circadian period. Oscillations of serum iron, TSAT, hepatic Tfrc, and erythropoietic activity were ablated when circadian machinery was disrupted in Bmal1 knockout mice. Interestingly, we find that circadian oscillations of erythropoietic activity and hepatic Tfrc expression are maintained in opposing phase, likely allowing for optimized usage and storage of serum iron whilst maintaining adequate serum levels and TSAT. This study provides the first confirmatory evidence that serum iron is circadian regulated, discerns circadian rhythms of TSAT, a widely used clinical marker of iron status, and uncovers liver-specific circadian regulation of TFR1, a major player in cellular iron uptake.

Generating tailored high frequency features in core collapse supernova gravitational wave signals applicable in LIGO interferometric studies

In this article, we introduce a methodology based on an analytical model of a damped harmonic oscillator subject to random forcing to generate transient gravitational wave signals. Such a model incorporates a simulated linear high-frequency component that mirrors the growing characteristic frequency over time observed in numerical simulations of core-collapse supernova gravitational wave signals. Unlike traditional numerical simulations, the method proposed in this study requires minimal computational resources, which makes it particularly advantageous for tasks such as data analysis, detection, and reconstruction of gravitational wave transients. To verify the physical accuracy of the generated signals, they are compared against the amplitude spectral of current LIGO interferometers and a 3D numerical simulation of a core-collapse supernova gravitational wave signal from the Andresen et al. 2017 model s15.nr. The results indicate that this approach is effective in generating scalable signals that align with LIGO interferometric data, offering potential utility in various gravitational wave transient investigations.