Harmonic Oscillator Frequency Research Articles

Observational signature of QPOs with particle motion around non-commutative Schwarzschild black hole surrounded by perfect fluid dark matter

We analyze the orbital and oscillatory motion of test particles in the vicinity of a non-commutative black hole submerged in perfect fluid dark matter and derive analytical solutions for the specific angular momentum and radial profiles of energy. Using the effective potential approach, we discuss the stability of circular orbits. Furthermore, we calculate the innermost stable circular orbits. The effective force acting on particles has also been discussed. We find the expressions for frequencies of radial and latitudinal harmonic oscillations as a function of the black hole mass and the model’s parameters. The key features of quasi-periodic oscillations of test particles near the stable circular orbits in an equatorial plane of the black hole are discussed. Furthermore, Periastron precession has been discussed. We demonstrate that the parameters of the model have a strong influence on particle motion around black holes. By using the observational data of four different X-ray binary systems GRO J1655-40, XTE J1550-564, XTE J1859+226, and GRS 1915+105, within the scope of Monte Carlo Markov Chain, we constrain the involved parameters α and β. It is necessary to mention that our presented investigations through graphical behavior are viable with required physical behavior.

Orbital motion, epicyclic oscillations, and collision of particles around conformally coupled charged black hole

The orbital and oscillatory motion of test particles around a non-rotating, conformally coupled charged black hole with scalar hair is studied in this work. The impact of the black hole parameters on particle motion is investigated. The stable circular orbits, specific angular momentum, and radial profiles with specific energy are computed using an analytical approach. We discuss the stability of circular orbits using the effective potential technique. We also compute the effective force and innermost stable circular orbits around a conformally connected charged black hole with scalar hair. In addition, we display the trajectories of particles around a conformally connected charged black hole with scalar hair and numerically integrate the equations of motion for the test particle. Additionally, we determine the formulae for the frequencies of latitudinal and radial harmonic oscillations about the mass of the black hole and the model’s parameters. The main characteristics of quasi-periodic oscillations close to stable circular orbits in the black hole’s equatorial plane are examined for test particles. Furthermore, the Periastron precession process is explored. We show particle motion around black holes strongly depends on the model parameters. It is important to note that the graphical behavior describing our findings is viable.

Particle dynamics with trajectories and epicyclic oscillations around a piece-wise black hole immersed in dark matter

We investigate the dynamics of neutral test particles revolving around a non-rotating black hole immersed in dark matter DM. We derive exact solutions for the radial profiles of specific angular momentum and energy for equatorial stable circular orbits as a function of the parameters of the black hole. Using the effective potential approach, we explore the stability of these circular orbits and the effective force acting on particles in the presence of dark matter. Additionally, we examine the impact of dark matter on the innermost stable circular orbits. By numerically integrating the equations of motion, we plot the trajectories of particles around the black hole and analyze how dark matter affects these trajectories. We also calculate the analytical frequencies of radial and latitudinal harmonic oscillations as functions of the dark matter parameter for both local and distant observers. We compare these results with scenarios where dark matter is absent. Furthermore, we study the effects of dark matter on periastron precession. We present an analysis of the constraints on the dark matter and black hole mass parameters using Markov Chain Monte Carlo (MCMC) methods. Our study focuses on QPOs observed in X-ray binaries, in particular, the microquasars GRO J1655-40 and XTE J1550-564, and the centers of the galaxies M82 X-1 and Sgr A⁎. We also analyze the particle collisions, discussing the center-of-mass energy of the colliding particles. Our observations reveal that the motion of particles revolving around the black hole is significantly affected by varying the model parameters.

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.

Bound states of relativistic spinless particles in a mix of circularly symmetric vector and scalar harmonic oscillators

We study the dynamics of relativistic spinless particles moving in a plane when there is circular symmetry. The general formalism for solving the Klein–Gordon equation in cylindrical coordinates for such systems is presented, as well as the conserved observables and the corresponding quantum numbers. We look for bound solutions of the corresponding Klein–Gordon equation when one has vector and scalar circularly symmetric harmonic oscillator potentials. Both positive and negative bound solutions are considered when there is either equal vector and scalar potentials or symmetric vector and scalar potentials, and it is shown how both cases are related through charge conjugation. We compute the non-relativistic limit for those cases, and show that for symmetric scalar and vector potentials the limit does not exist in the first order of an harmonic oscillator frequency, recovering a known result from the Dirac equation with the same kind of potentials.

Lewis and berry phases for a gravitational wave interacting with a quantum harmonic oscillator

In this work, we compute the Lewis and Berry phases for a gravitational wave interacting with a two dimensional quantum harmonic oscillator in the transverse-traceless gauge. We have considered a gravitational wave consisting of the plus polarization term only. Considering the cross polarization term to be absent makes the Hamiltonian separable in terms of the first and the second spatial coordinates. We then compute the Lewis phase by assuming a suitable form of the Lewis invariant considering only quadratic order contributions from both position and momentum variables. Next, we obtain two Lewis invariants corresponding to each separable part of the full Hamiltonian of the system. Using both Lewis invariants, one can obtain two Ermakov-Pinney equations, from which we finally obtain the corresponding Lewis phase. Then making an adiabatic approximation enables us to isolate the Berry phase for the full system. After this we obtain some explicit expressions of the Berry phase for a plane polarized gravitational wave with different choices of the harmonic oscillator frequency. Finally, we consider a gravitational wave with cross polarization only interacting with an isotropic two dimensional harmonic oscillator. For this we obtain the Lewis phase and the total Berry phase of the system, which is found to be dependent upon the cross polarization part of the gravitational wave.

Orbital motion and quasi-periodic oscillations with periastron and Lense–Thirring precession of slowly rotating Einstein–Æther black hole

We study the orbital and oscillatory motion of test particles moving around slowly rotating first and second kinds of Einstein–Æther black holes. In relation to the black hole parameters, we find analytical solutions for the radial profiles of specific energy and specific angular momentum of the equatorial stable circular orbits. The properties of the co-rotating as well as contra-rotating innermost stable circular orbits are analyzed. We examine the radial profiles of the frequencies of latitudinal and radial harmonic oscillations as a function of the black hole mass and dimensionless coupling constants of the theory. The key features of quasi-periodic oscillations of test particles near the stable circular orbits in an equatorial plane of the black hole are discussed. We investigate the positions of resonant radii for high-frequency quasi-periodic oscillations models, namely epicyclic resonance and its variants, relativistic precession and its variants, tidal disruption, as well as warped disc models, considered in the background of slowly rotating first and second kinds of slowly rotating Einstein–Æther black holes. Furthermore, Periastron and Lense–Thirring precessions have been discussed. We demonstrate that the dimensionless coupling parameters of the theory have a strong influence on particle motion around Einstein–Æther black holes.

Ab initio no-core shell-model description of C10–14 isotopes

We present a systematic study of the $^{10--14}\mathrm{C}$ isotopes within the ab initio no-core shell-model theory. We apply four different realistic nucleon-nucleon $(NN)$ interactions: (i) the charge-dependent Bonn 2000 (CDB2K) potential; (ii) the inside nonlocal outside Yukawa (INOY) potential; (iii) the next-to-next-to-next-to-leading order $({\mathrm{N}}^{3}\mathrm{LO})$ potential; and (iv) the optimized next-to-next-to-leading order $({\mathrm{N}}^{2}{\mathrm{LO}}_{\mathrm{opt}})$ potential. We report the low-lying energy spectra of both positive- and negative-parity states for $^{10--14}\mathrm{C}$ isotopes and investigate the level structures. We also calculate electromagnetic properties such as transition strengths, quadrupole moments, and magnetic moments. The dependence of point-proton radii on the harmonic-oscillator frequency and basis space is shown. We present calculations of the translation invariant one-body density matrix in the no-core shell-model and discuss isotopic trends in the density distribution. The maximum basis space reached is $10\ensuremath{\hbar}\mathrm{\ensuremath{\Omega}}$ for $^{10}\mathrm{C}$ and $8\ensuremath{\hbar}\mathrm{\ensuremath{\Omega}}$ for $^{11--14}\mathrm{C}$, with a maximum M-scheme dimension of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{9}$ for $^{10}\mathrm{C}$. We found that, while the INOY interaction gives the best description of the ground-state energies, the ${\mathrm{N}}^{3}\mathrm{LO}$ interaction best reproduces the point-proton radii.

Using asymptotic homogenization to determine effective thermo-viscoelastic properties of fibrous composites with interphase layer

In this paper, we apply the method of asymptotic homogenization in parametric space in order to determine thermo-viscoelastic properties of materials composed of cylindrical fibers surrounding by an intermediate layer separating them from viscoelastic matrix. We use the Maxwell model of viscoelasticity. The volumetric fraction and physical properties of the layer can vary. There is a possibility of a contrast between the properties of fibers, the layer, and the matrix. Our approach allows us to treat temperature as a parameter and study the response of mechanical characteristics on the change in temperature. We perform the Fourier transform of governing equations and then implement asymptotic homogenization of the resulting equations in parametric space. Microscopic boundary value problem is defined on a periodic cell consisting of a fiber surrounded by a layer and embedded in the matrix. Macroscopic equations are derived for the complex Young’s and shear moduli. Effective viscoelastic properties of the material are computed for different values of the frequency of harmonic oscillations and for various temperatures. This paper discusses how effective storage and loss Young’s and shear moduli depend on volumetric fraction and mechanical properties of the material of the layer. The obtained results can provide information on how concentration, structure and properties of inclusions can affect the effective storage and loss Young’s and shear moduli.

Dynamics of quantum droplets in an external harmonic confinement

Recent theoretical and experimental results show that one-dimensional (1D) weakly interacting atomic Bose-Bose mixtures with repulsive interspecies mean field (MF) interaction are stabilized by attractive quadratic beyond-mean-field (BMF) effects into self-bound quantum droplet (QD) in free space. Here, we construct an exact analytical model to investigate the structure and dynamics of QDs in presence of external harmonic confinement by solving the 1D extended Gross–Pitäevskii equation (eGPE) with temporal variation of MF and BMF interactions. The model provides the analytical form of wavefunction, phase, MF and BMF nonlinearities. The generation of QDs and interesting droplet to soliton transition in presence of regular/expulsive parabolic traps by taking the comparable MF and BMF interactions are illustrated. We derive the phase diagram of the droplet-soliton phase transition between amplitude of MF, BMF interactions and harmonic oscillator frequency. The strength and form of oscillator frequency are identified as key parameter for tuning the compression, fragmentation and transport of droplets. Finally, the stability of the obtained solutions are confirmed from Vakhitov–Kolokolov (VK) criterion and are found stable.

Phonon spectra of a two-dimensional solid dusty plasma modified by two-dimensional periodic substrates.

Phonon spectra of a two-dimensional (2D) solid dusty plasma modulated by 2D square and triangular periodic substrates are investigated using Langevin dynamical simulations. The commensurability ratio, i.e., the ratio of the number of particles to the number of potential well minima, is set to 1 or 2. The resulting phonon spectra show that propagation of waves is always suppressed due to the confinement of particles by the applied 2D periodic substrates. For a commensurability ratio of 1, the spectra indicate that all particles mainly oscillate at one specific frequency, corresponding to the harmonic oscillation frequency of one single particle inside one potential well. At a commensurability ratio of 2, the substrate allows two particles to sit inside the bottom of each potential well, and the resulting longitudinal and transverse spectra exhibit four branches in total. We find that the two moderate branches come from the harmonic oscillations of one single particle and two combined particles in the potential well. The other two branches correspond to the relative motion of the two-body structure in each potential well in the radial and azimuthal directions. The difference in the spectra between the square and triangular substrates is attributed to the anisotropy of the substrates and the resulting alignment directions of the two-body structure in each potential well.

Rapid Quantum Squeezing by Jumping the Harmonic Oscillator Frequency.

Quantum sensing and quantum information processing use quantum advantages such as squeezed states that encode a quantity of interest with higher precision and generate quantum correlations to outperform classical methods. In harmonic oscillators, the rate of generating squeezing is set by a quantum speed limit. Therefore, the degree to which a quantum advantage can be used in practice is limited by the time needed to create the state relative to the rate of unavoidable decoherence. Alternatively, a sudden change of harmonic oscillator's frequency projects a ground state into a squeezed state which can circumvent the time constraint. Here, we create squeezed states of atomic motion by sudden changes of the harmonic oscillation frequency of atoms in an optical lattice. Building on this protocol, we demonstrate rapid quantum amplification of a displacement operator that could be used for detecting motion. Our results can speed up quantum gates and enable quantum sensing and quantum information processing in noisy environments.

Fundamental limits and optimal estimation of the resonance frequency of a linear harmonic oscillator

All physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses assuming specific ways of estimating frequency can underestimate the available precision and overlook unconventional measurement regimes. Here we derive a general, estimation-method-independent Cramer Rao lower bound for a linear harmonic oscillator resonance frequency measurement uncertainty, seamlessly accounting for the quantum, thermodynamic and instrumental limitations, including Fisher information from quantum backaction- and thermodynamically driven fluctuations. We provide a universal and practical maximum-likelihood frequency estimator reaching the predicted limits in all regimes, and experimentally validate it on a thermodynamically limited nanomechanical oscillator. Low relative frequency uncertainty is obtained for both very high bandwidth measurements (≈10−5 for τ = 30 μs) and measurements using thermal fluctuations alone (<10−6). Beyond nanomechanics, these results advance frequency-based metrology across physical domains.

Anharmonic oscillator: a playground to get insight into renormalization

In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used in quantum field theory (QFT) where the bare values of the parameters of the theory run when an interaction is added. In this paper, we review some of these techniques and introduce some new ones in line with QFT methods. Moreover, we investigate the case of more than one oscillator to see how the frequencies of small oscillations change when non-linear terms are added to a linear system and observe an interesting beat phenomenon in degenerate coupled oscillatory systems.

Zero absolute vorticity state in thermal equilibrium as a hydrodynamic analog of the quantum harmonic oscillator ground state

Here, we point out on an intriguing mapping between the quantum harmonic oscillator ground state and the zero absolute vorticity plane Couette flow of a Boltzmann-like density distributed ideal gas in thermal equilibrium. The mapping is obtained when the gas is embedded in a rotating frame whose rotation rate is equal to half of the frequency of the quantum harmonic oscillator.

Photon-recoil and laser-focusing limits to Rydberg gate fidelity

Limits to Rydberg gate fidelity that arise from the entanglement of internal states of neutral atoms with the motional degrees of freedom due to the momentum kick from photon absorption and re-emission is quantified. This occurs when the atom is in a superposition of internal states but only one of these states is manipulated by visible or UV photons. The Schr\"odinger equation that describes this situation is presented and two cases are explored. In the first case, the entanglement arises because the spatial wave function shifts due to the separation in time between excitation and stimulated emission. For neutral atoms in a harmonic trap, the decoherence can be expressed within a sudden approximation when the duration of the laser pulses are shorter than the harmonic oscillator period. In this limit, the decoherence is given by simple analytic formulas that account for the momentum of the photon, the temperature of the atoms, the harmonic oscillator frequency, and atomic mass. In the second case, there is a reduction in gate fidelity because the photons causing absorption and stimulated emission are in focused beam modes. This leads to a dependence of the optically induced changes in the internal states on the center of mass atomic position. In the limit where the time between pulses is short, the decoherence can be expressed as a simple analytic formula involving the laser waist, temperature of the atoms, the trap frequency and the atomic mass. These limits on gate fidelity are studied for the standard $\pi-2\pi-\pi$ Rydberg gate and a new protocol based on a single adiabatic pulse with Gaussian envelope.

Deep Reinforcement Learning Control of Cylinder Flow Using Rotary Oscillations at Low Reynolds Number

We apply deep reinforcement learning to active closed-loop control of a two-dimensional flow over a cylinder oscillating around its axis with a time-dependent angular velocity representing the only control parameter. Experimenting with the angular velocity, the neural network is able to devise a control strategy based on low frequency harmonic oscillations with some additional modulations to stabilize the Kármán vortex street at a low Reynolds number Re=100. We examine the convergence issue for two reward functions showing that later epoch number does not always guarantee a better result. The performance of the controller provide the drag reduction of 14% or 16% depending on the employed reward function. The additional efforts are very low as the maximum amplitude of the angular velocity is equal to 8% of the incoming flow in the first case while the latter reward function returns an impressive 0.8% rotation amplitude which is comparable with the state-of-the-art adjoint optimization results. A detailed comparison with a flow controlled by harmonic oscillations with fixed amplitude and frequency is presented, highlighting the benefits of a feedback loop.

Simulating fermions in spin-dependent potentials with spin models on an energy lattice

We study spin-1/2 fermions in spin dependent potentials under the \emph{spin model approximation}, in which interatomic collisions that change the total occupation of single-particle modes are ignored. The spin model approximation maps the interacting fermion problem to an ensemble of lattice spin models in energy space, where spin-spin interactions are long-ranged and spin-anisotropic. We show that the spin model approximation is accurate for weak interactions compared to the harmonic oscillator frequency, and captures the collective spin dynamics to timescales much longer than would be expected from perturbation theory. We explore corrections to the spin model, and the relative importance of corrections when realistic anharmonic potential corrections are taken into account. Additionally, we present numerical techniques that are useful for analysis of spin models on an energy lattice, including enacting a change of single-particle basis on a many-body state as an effective time evolution, and fitting of spatially inhomogeneous long-range interactions with exponentials. This latter technique is useful for constructing matrix product operators for use in DMRG analyses, and may have broader applicability within the tensor network community.

Realistic analytical approach for α decay and clustering

We approximate the realistic $\ensuremath{\alpha}$-core nuclear interaction between the inner turning point and Coulomb barrier, derived within the double folding procedure, by a parabolic dependence. It turns out that the corresponding harmonic oscillator frequency is concentrated in a narrow interval around $\ensuremath{\hbar}{\ensuremath{\omega}}_{1}\ensuremath{\approx}$ 9 MeV for all analyzed transitions from even-even and odd-mass $\ensuremath{\alpha}$ emitters. The penetrability through the nuclear barrier has an exponential dependence on the ratio between the fragmentation potential and this harmonic oscillator frequency. On the other hand, the Coulomb penetrability has the standard dependence on the Coulomb parameter. Our analysis revealed that the reduced width, extracted by using the nuclear plus Coulomb penetrability factors, exponentially decreases versus the number of $\ensuremath{\alpha}$ clusters along all analyzed $\ensuremath{\alpha}$ lines, except one region where it increases by approaching the neutron magic number ${N}_{\mathrm{mag}}=126$. In that case, the number of valence proton pairs is much smaller than the number of valence neutron pairs. The reduced width exponentially depends on the magic neutron-proton asymmetry above doubly magic nuclei. These dependencies allow us to propose a systematics for reduced widths in terms of the quartet number and magic asymmetry evaluated above the closest doubly magic nuclei.

Automation of vibration modes of soil compaction machines

The relevance of high-quality compaction of soil foundations during the construction of embankments and foundations during the construction of engineering structures is given. An effective vibrodynamic method of compaction of gravel and sand materials for foundations of building structures for various purposes is substantiated and proposed. The method of continuous monitoring of the degree of compaction of the soil by measuring the magnitudes of the amplitudes and frequencies of harmonic oscillations of the compacted surface is determined. A schematic diagram of the automatic control system CAP of vibration modes of shock-absorbing soil compacting machines with a crank-oscillating exciter is proposed. The principle of regulating the operating modes of a vibrating machine using an automatic control pulse distributor is stated. A structural block diagram of the CAP elements is constructed and an analysis of the dynamic properties that determine the optimal control time is carried out. The main elements of the CAP are determined and their work in the control program is shown: the frequency of impact of the working mechanism on the soil surface being compacted, depending on the degree of compaction. Key words: soil compaction degree, operating mechanism, amplitude and frequency of harmonic oscillations of the surface of the soil being compacted, vibro-shock machines with a crank-connecting rod exciter, automatic control system, control pulse distributor, process parameters sensors, on-board microprocessor controller.