Harmonic Oscillator Research Articles

Violation of the two-time Leggett-Garg inequalities for a harmonic oscillator

Violation of the two-time Leggett-Garg inequalities for a harmonic oscillator

Making two particle detectors in flat spacetime communicate quantumly

A communication protocol with nonzero quantum capacity is found when the two communicating parts are particle detector models in (3+1)-dimensional spacetime. In particular, as detectors, we consider two harmonic oscillators interacting with a scalar field, whose evolution is generalized for whatever background spacetime and whatever spacetime smearing of the detectors. We then specialize to Minkowski spacetime and an initial Minkowski vacuum, considering a rapid interaction between the field and the two detectors, studying the case where the receiver is static and the sender is moving. The possibility to have a quantum capacity greater than zero stems from a relative acceleration between the detectors. Indeed, no reliable quantum communication is possible when the two detectors are static or moving inertially with respect to each other, but a reliable quantum communication can be achieved between a uniformly accelerated sender and an inertial receiver. Published by the American Physical Society 2024

Periodic solutions for a class of asymptotically linear damped vibration problems with resonance at infinity

Periodic solutions for a class of asymptotically linear damped vibration problems with resonance at infinity

Improvement of shoulder peak effect in graphene/silicone rubber strain sensors by nanosilica

Conducting polymer composites (CPCs) typically exhibit shoulder peak phenomena in their resistive response signals, which greatly limits their practical application as strain sensors in the field of vibration damping. In this paper, nanosilica (SiO2) nanoparticles were incorporated into graphene (GR)/methyl vinyl silicone rubber (VMQ) composites to obtain the optimum content of SiO2 to eliminate the shoulder peak phenomenon. The results showed that the shoulder peak phenomenon of the resistance response signal of the composites disappeared after the addition of 30 % SiO2, which explained the mechanism of eliminating the shoulder peak phenomenon. Meanwhile, the tensile strength and Young's modulus of the composites were improved, and excellent resistance-strain response properties were obtained, including a wide sensing range (＞200 %), high sensitivity (GF = 839.02), fast response time (37 ms), and good durability and stability (9000 cycles at 50 % strain). It shows that the strain sensor has great potential for health monitoring in the field of vibration damping.

Study of the Vibration Isolation Properties of a Pneumatic Suspension System for the Seat of a Working Machine with Adjustable Stiffness

This paper presents a study of the vibration isolation properties of pneumatic suspension systems for work machinery seats, with a particular focus on adjustable stiffness. It highlights the contribution that semi-active seat suspension systems make to vibration reduction, ultimately leading to improved passenger comfort levels and increased safety for vehicle users. The primary objectives of the research were twofold: firstly, to identify the key parameters of the apneumatic vibration isolation system; and secondly, to evaluate its performance in improving vibration damping. This entailed the development of a mathematical model that would foreground the movement through simulations based on different initial pressures, thus enabling the accurate prediction of real-life scenarios concerning the vibration-damping characteristics of the seating system, taking into account the different design options available for working machine technology applied at the test bed level, of which the pneumatic isolator is an integral component. In the cognitive process, the verification and validation of the formulated theoretical model play an important role. This approach enables the behaviour of the actual system to be inferred from the results of simulation studies, thus allowing the design of an appropriate vibration control system. By simulating different air bellow pressures, the characteristics of the seat suspension system can be assessed. This study provides valuable insights into optimising the vibration-damping capability of the air suspension system.

Non-linear MHD investigations of high-confinement regimes without type-I ELMs in ASDEX Upgrade and JT-60SA

Large edge localised modes (ELMs) would cause an unacceptable reduction of material lifetime in future large tokamaks due to the significant amount of energy expelled from the magnetically confined region towards the plasma facing components. Thoroughly validated modelling of regimes devoid of large ELMs is crucial as it may then provide predictive insights prior to tokamak operation and design. This paper describes recent efforts pursued with the non-linear extended MHD code JOREK in the modelling of three scenarios without large ELMs: quiescent H-mode (QH-mode), quasi-continuous exhaust regime (QCE regime), and the enhanced D-alpha H-mode (EDA H-mode). For each of these regimes, the non-linear dynamics observed in the simulations are detailed and compared to experimental observations of the underlying instabilities of each regime (edge harmonic oscillation for QH-mode, small ELMs for QCE regime, and quasi-coherent mode for EDA H-mode). For QH-mode, the kink-peeling mode is found to govern the dynamics and a transition to a large ELM is obtained above the same density threshold as in the modelled experiment. For the QCE regime and EDA H-mode, resistive peeling–ballooning modes dominate and pedestal fluctuation frequencies correspond well to experimental observations. The dominant mechanisms for the excitation and suppression of these instabilities are presented and their influence on simulation dynamics is shown. Finally, predictive simulations of edge instabilities at different values of plasma resistivity in a 4.60 MA scenario with low edge safety factor in JT-60SA are presented.

Study on damping performance of non-ideal particle-tuned inerter damper

Aiming at the shortcomings of the current particle dampers and the needs of civil engineering vibration damping, while considering the damping in the non-ideal inertial vessel, a new type of non-ideal particle tuned inerter damper (NPTID) is proposed. Firstly, the construction and technical realization of NPTID are introduced, the mechanical model of NPTID is proposed based on the principle of energy dissipation by particle collision, and the motion control equations of the single-degree-of-freedom structure with an additional NPTID are established; then three natural seismic waves and one artificial seismic wave are selected as the external excitations, and the damping performance of the NPTID is analyzed; finally, the influence of key parameters on the control effect of the NPTID is investigated by parametric analysis. The results show that NPTID has good control effect, and can realize the reduction ratio of more than 43% by utilizing a 0.1% particle mass ratio.

Ground State Homoclinic Solutions for Damped Vibration Systems with Periodicity

Ground State Homoclinic Solutions for Damped Vibration Systems with Periodicity

Cyanonaphthalene and cyanonaphthyl radicals: Vibrational structures via computed negative ion photoelectron spectra and thermochemistry of 1- and 2-cyanonaphthalene.

A double harmonic oscillator model is applied to compute the negative ion photoelectron spectra (NIPES) of the 1- and 2-cyanonaphthalene (CNN) radical anions. The computed Franck-Condon factors utilize optimized structures and harmonic vibrational frequencies obtained using density functional theory with the B3LYP 6-311++G (2d,2p) basis set while considering the mode-mixing Duschinsky effects. To test the accuracy of our model, the NIPES of α and β naphthyl radical anions were computed, and a strong agreement between the slow electron velocity-map ion imaging spectra and the predicted spectra was found. The adiabatic electron affinities (EAs) of the ground singlet states (S0) in 1-CNN and 2-CNN are 0.856 and 0.798eV, respectively. The origin of the lowest-lying triplet (T1) states in 1-CNN and 2-CNN is found to be 3.226 and 3.266eV, resulting in singlet-triplet energy splittings (ΔEST) of 2.370 and 2.468eV, respectively. Both the NIPES for electron detachment to the S0 and T1 states exhibit well-resolved vibrational features, allowing for the assignment of several vibrational fundamental frequencies. Following deprotonation, several isomers are formed, with the most stable deprotonated radical anions in 1-CNN and 2-CNN, corresponding to the removal of the most acidic proton, with EAs of 2.062 and 2.16eV. The rich spectroscopic and thermochemical data obtained in the current study make the CNN radical anions and their deprotonated species interesting systems for investigation in gas-phase, negative-ion experiments.

Axion magnetic resonance: A novel enhancement in axion-photon conversion

We identify a new resonance, axion magnetic resonance, that can greatly enhance the conversion rate between axions and photons. A series of axion search experiments rely on converting them into photons inside a constant magnetic field background. A common bottleneck of such experiments is the conversion amplitude being suppressed by the axion mass when ma≳10−4 eV. We point out that a spatial or temporal variation in the magnetic field can cancel the difference between the photon dispersion relation and that of the axion, hence greatly enhancing the conversion probability. We demonstrate that the enhancement can be achieved by both a helical magnetic field profile and a harmonic oscillation of the magnitude. Our approach can extend the projected ALPS II reach in the axion-photon coupling (gaγ) by two orders of magnitude at ma=10−3 eV with moderate assumptions (see .) Published by the American Physical Society 2024

Gauged permutation invariant matrix quantum mechanics: partition functions

The Hilbert spaces of matrix quantum mechanical systems with N × N matrix degrees of freedom X have been analysed recently in terms of SN symmetric group elements U acting as X → UXUT. Solvable models have been constructed uncovering partition algebras as hidden symmetries of these systems. The solvable models include an 11-dimensional space of matrix harmonic oscillators, the simplest of which is the standard matrix harmonic oscillator with U(N) symmetry. The permutation symmetry is realised as gauge symmetry in a path integral formulation in a companion paper. With the simplest matrix oscillator Hamiltonian subject to gauge permutation symmetry, we use the known result for the micro-canonical partition function to derive the canonical partition function. It is expressed as a sum over partitions of N of products of factors which depend on elementary number-theoretic properties of the partitions, notably the least common multiples and greatest common divisors of pairs of parts appearing in the partition. This formula is recovered using the Molien-Weyl formula, which we review for convenience. The Molien-Weyl formula is then used to generalise the formula for the canonical partition function to the 11-parameter permutation invariant matrix harmonic oscillator.

Correlation between destructive and non-destructive evaluation to study of plastic waste aggregate mortar: a case study of mechanical proprieties

Non-destructive evaluation using ultrasonic pulse velocity (UPV) testing has extensive applications in the cement materials industry. Ultrasonic pulse velocity (UPV) test is accepted as alternative to destructive testing to determine the compressive strength, dynamic modulus of elasticity, and Poisson’s ratio, which are needed for structural design. In modern construction technology, the use of Plastic waste (PW) as a partial replacement to natural aggregates in a mortar mix is growing in popularity primarily because it reduces the initial capital cost of raw materials and the associated conservation in environment. In this regard, this study explains the correlations between mechanical proprieties, and UPV tests for mortar contains 25%, 50%, and 75% of waste aggregate of plastic. Mortar based on Plastic Waste (MPW) specimens were tested by direct, semi-direct, and indirect UPV. UPV measurements can be effectively used to determine the dynamic modulus of elasticity and Poisson’s ratio of Mortar based on Plastic Waste MPW. The dynamic elastic modulus and the Poisson’s ratio decreases for the same mortar composite when at increasing PW content. Thus, the incorporation of PW particles into the cement matrix confirms the capacity of composites to reduce the sound intensity and damp vibrations inside the composites. The results of this study will be significant for non-destructive evaluations of MPW, while additional recommendations for future studies are presented at the end of the paper.

Design and Simulation of Adiabatic–Damping Dual–Function Strut for LH2 Storage Tank

In the process of the on–board transportation of liquid hydrogen storage and transportation tanks, apart from considering the support strength and adiabatic performance, it is imperative to take into account the vibration characteristics of the carrying platform. The present work introduces a versatile support structure comprising a damping module and a ball contact insulation structure, enabling effective isolation of external vibrations while simultaneously providing support and insulation. The first step involves describing the principle of a flexible support structure and designing the mechanical structure. Subsequently, a damping analysis is conducted based on dynamic theory to establish the relationship between the spring and damping. Finally, the structural parameters of the dual–function strut are determined, followed by simulation of heat transfer performance. The results demonstrate that the dual–function strut exhibits exceptional vibration damping performance by reducing the amplitude of external vibrations greater than 5 Hz to less than 6%. Moreover, owing to the compact linear diameter spring structure of the vibration damping module and its ball contact effect, the thermal resistance of the dual–function strut is significantly enhanced, resulting in a mere heat leakage of only 22 W/m2 in a single rod section.

Quantized Microcavity Polariton Lasing Based on InGaN Localized Excitons.

Exciton-polaritons, which are bosonic quasiparticles with an extremely low mass, play a key role in understanding macroscopic quantum effects related to Bose-Einstein condensation (BEC) in solid-state systems. The study of trapped polaritons in a potential well provides an ideal platform for manipulating polariton condensates, enabling polariton lasing with specific formation in k-space. Here, we realize quantized microcavity polariton lasing in simple harmonic oscillator (SHO) states based on spatial localized excitons in InGaN/GaN quantum wells (QWs). Benefiting from the high exciton binding energy (90 meV) and large oscillator strength of the localized exciton, room-temperature (RT) polaritons with large Rabi splitting (61 meV) are obtained in a strongly coupled microcavity. The manipulation of polariton condensates is performed through a parabolic potential well created by optical pump control. Under the confinement situation, trapped polaritons are controlled to be distributed in the selected quantized energy sublevels of the SHO state. The maximum energy spacing of 11.3 meV is observed in the SHO sublevels, indicating the robust polariton trapping of the parabolic potential well. Coherent quantized polariton lasing is achieved in the ground state of the SHO state and the coherence property of the lasing is analyzed through the measurements of spatial interference patterns and g(2)(τ). Our results offer a feasible route to explore the manipulation of macroscopic quantum coherent states and to fabricate novel polariton devices towards room-temperature operations.

The Radiation Field, at the Origin of the Quantum Canonical Operators

We show that the electromagnetic radiation field, conventionally introduced as a perturbation in quantum mechanics, is actually at the basis of the operator formalism. We first analyze the linear resonant response of the (continuous) variables x(t), p(t) of a harmonic oscillator to the full radiation field, i.e. the zero-point field plus an applied field playing the role of the driving force, and then extend the analysis to the response of a charged particle bound by a non-linear force, typically an atomic electron. This leads to the establishment of a one-to-one correspondence between the response functions and the respective quantum operators, and to the identification of the quantum commutator with the Poisson bracket of the response functions with respect to the normalized variables of the driving field. To complete the quantum description, a similar procedure is used to obtain the field operators as the response functions to the same normalized variables. The results allow us to draw important conclusions about the physical content of the quantum formalism, in particular about the meaning of the quantum expectation values and the coarse-grained nature of the quantum-mechanical description.

Mimicking classical noise in ion channels by quantum decoherence

The mechanism of selectivity in ion channels is still an open question in biology. Recent studies suggest that the selectivity filter may exhibit quantum coherence, which could help explain how ions are selected and conducted. However, environmental noise causes decoherence and loss of quantum effects. It is hoped that the effect of classical noise on ion channels can be modeled using the framework provided by quantum decoherence theory. In this paper, the behavior of the ion channel system was simulated using two models: the Spin–Boson model and the stochastic Hamiltonian model under classical noise. Additionally, using a different approach, the system’s evolution was modeled as a two-level Spin–Boson model with tunneling, interacting with a bath of harmonic oscillators, based on decoherence theory. We investigated under what conditions the decoherence model approaches and deviates from the noise model. Specifically, we examined Gaussian noise and Ornstein-Uhlenbeck noise in our model. Gaussian noise shows a very good agreement with the decoherence model. By examining the results, it was found that the Spin–Boson model at a high hopping rate of potassium ions can simulate the behavior of the system in the classical noise approach for Gaussian noise.

Quantum gravity signatures in gravitational wave detectors placed inside a harmonic trap potential

In this work, we consider a general gravitational wave detector of gravitational waves interacting with an incoming gravitational wave carrying plus polarization only placed inside a harmonic trap. This model can be well acquainted with the description of a resonant detector of gravitational waves as well. The well-known detector-gravitational wave interaction scenario uses the method of a semiclassical approach where the detector is treated quantum mechanically but the gravitational wave is considered at a classical level. In our analysis, we use a discrete mode decomposition of the gravitational wave perturbation which results in a Hamiltonian involving the position and momentum operators corresponding to the gravitational wave and the harmonic oscillator. We have then calculated the transition probability for the harmonic oscillator-gravitational wave tensor product state for going from an initial state to some unknown final state. Using the energy flux relation of the gravitational waves, we observe that if we consider the total energy as a combination of the number of gravitons in the initial state of the detector then the transition probability for the resonant absorption case scenario takes the analytical form which is exactly similar to the semiclassical absorption case. In the case of the emission scenario, we observe a spontaneous emission of a single graviton which was completely absent in the semiclassical analog of this model. This therefore gives a direct signature of linearized quantum gravity. Published by the American Physical Society 2024

Neural canonical transformations for vibrational spectra of molecules.

The behavior of polyatomic molecules around their equilibrium positions can be regarded as that of quantum-coupled anharmonic oscillators. Solving the corresponding Schrödinger equations enables the interpretation or prediction of the experimental spectra of molecules. In this study, we developed a novel approach for solving the excited states of anharmonic vibrational systems. The normal coordinates of the molecules are transformed into new coordinates through a normalizing flow parameterized by a neural network. This facilitates the construction of a set of orthogonal many-body variational wavefunctions. This methodology has been validated on an exactly solvable 64-dimensional coupled harmonic oscillator, yielding numerical results with a relative error of 10-6. The neural canonical transformations are also applied to calculate the energy levels of two specific molecules, acetonitrile (CH3CN) and ethylene oxide (C2H4O). These molecules involve 12 and 15 vibrational modes, respectively. A key advantage of this approach is its flexibility concerning the potential energy surface, as it requires no specific form. Furthermore, this method can be readily implemented on large-scale distributed computing platforms, making it easy to extend to investigating complex vibrational structures.

Orbital motion and epicyclic oscillations around Bardeen black hole surrounded by perfect fluid dark matter

We study the orbital and oscillatory motion of test particles moving around a rotating Bardeen black hole immersed in perfect fluid dark matter. We obtain the analytical solutions for the radial profiles of specific energy as well as the specific angular momentum of the equatorial stable circular orbits. Using the effective potential approach, we also discuss the stability of circular orbits. We compute the frequencies of radial and latitudinal harmonic oscillations as a function of mass, charge, and angular momentum of the black hole as well as the parameter describing the perfect fluid dark matter. The main characteristics of test particle quasi-periodic oscillations near stable circular orbits are examined in the equatorial plane. Furthermore, we study precessions of Periastron and Lense-Thirring. It is observed that the particle's motion around the black hole is strongly influenced by the model parameters.

Performance of Effective Harmonic Oscillator Approach for the Calculations of Vibrational Transition Energies of Large Molecules.

The accuracy and performance of the effective harmonic oscillator approximation for the description of anharmonic vibrational structure calculations are tested for large molecular systems and compared with experimental values along with vibrational self-consistent field and second-order perturbation theories. The effective harmonic oscillator approach is an effective single-particle approximation where the variational parameters are the centroids and widths of the multidimensional Gaussian product functions posited as the vibrational wave functions. A comprehensive calculation for 849 transitions that include the fundamentals, two and three quanta overtone transitions, and several combination bands of three polyaromatic hydrocarbons and one DNA nucleobase with a total of 231 normal modes are assessed. A comparison of EHO results with the experimental values is done for the polyaromatic hydrocarbons, and a close agreement is found between the two results. It also offers anharmonic eigenstates and eigenfunctions that are nearly identical with vibrational self-consistent field theory. An extensive analysis on the resultant wave functions of the excited states is performed. The overall root-mean-square deviation (RMSD) between these two methods for 849 transitions understudy is only about 8.3 cm-1, suggesting the effective harmonic oscillator as a viable alternative for the reliable calculations of transition energies of large molecular systems.