Harmonic Oscillator Frequency Research Articles

Quantum aspects of a moving magnetic quadrupole moment interacting with an electric field

The quantum dynamics of a moving particle with a magnetic quadrupole moment that interacts with electric and magnetic fields is introduced. By dealing with the interaction between an electric field and the magnetic quadrupole moment, it is shown that an analogue of the Coulomb potential can be generated and bound state solutions can be obtained. Besides, the influence of the Coulomb-type potential on the harmonic oscillator is investigated, where bound state solutions to both repulsive and attractive Coulomb-type potentials are achieved and the arising of a quantum effect characterized by the dependence of the harmonic oscillator frequency on the quantum numbers of the system is discussed.

Analytical Method of Determining Folded Depressed Shells’ Free Oscillation Frequency

The paper shows a conclusion and a solution of principal resolving equations of the motion of linear and geometrically non-linear theories of thin depressed shells with median surface breaks. A formula has been obtained for determining the shell’s free bending harmonic oscillation frequency in case of a hinge support on rigid diaphragms. Charts are supplied showing the dependence of free oscillation frequency on the change of different factors. A conclusion has been drawn concerning the analytical method efficiency.

NORMAL FORM AND ENERGY CONSERVATION OF HIGH FREQUENCY SUBSYSTEMS WITHOUT NONRESONANCE CONDITIONS

We consider a system in which some high frequency harmonic oscillators are coupled with a slow system. We prove that up to very long times the energy of the high frequency system changes only by a small amount. The result we obtain is completely independent of the resonance relations among the frequencies of the fast system. More in detail, denote by ϵ-1 the smallest high frequency. In the first part of the paper we apply the main result of [1] to prove almost conservation of the energy of the high frequency system over times exponentially long with ϵ-1/n (n being the number of fast oscillators). In the second part of the paper we give a new self-contained proof of a similar result which however is valid only over times of order ϵ-N with an arbitrary N. Such a second result is very similar to the main result of the paper [4], which actually was the paper which stimulated our work.

Shaking-induced dynamics of cold atoms in magnetic traps

We describe an experiment in which cold rubidium atoms, confined in an elongated magnetic trap, are excited by transverse oscillation of the trap centre. The temperature after excitation exhibits resonance as a function of the driving frequency. We measure these resonances at several different trap frequencies. In order to interpret the experiments, we develop a simple model that incorporates both collisions between atoms and the anharmonicity of the real three-dimensional trapping potential. As well as providing a precise connection between the transverse harmonic oscillation frequency and the temperature resonance frequency, this model gives insight into the heating and loss mechanisms, and into the dynamics of driven clouds of cold trapped atoms.

A Quasi-Lie Schemes Approach to Second-Order Gambier Equations

A quasi-Lie scheme is a geometric structure that provides t-dependent changes of variables transforming members of an associated family of systems of first-order differential equations into members of the same family. In this note we introduce two quasi-Lie schemes for studying second-order Gambier equations in a geometric way. This allows us to study the transformation of these equations into simpler canonical forms, which solves a gap in the previous literature, and other relevant differential equations, which leads to derive new constants of motion for families of second-order Gambier equations. Additionally, we describe general solutions of certain second-order Gambier equations in terms of particular solutions of Riccati equations, linear systems, and t-dependent frequency harmonic oscillators.

Adsorption and Dilational Rheology of Mixed β-Casein/DoTAB Layers Formed by Sequential and Simultaneous Adsorption at the Water/Hexane Interface

The interfacial behavior of β-casein (βCS) has been investigated in presence of the cationic surfactant dodecyl trimethyl ammonium bromide (DoTAB) at the water/hexane interface and compared to that obtained for the water/air interface. The used experimental technique is a drop profile analysis tensiometer specially equipped with a coaxial double capillary, which allows investigation of sequential adsorption of individual components besides the traditional simultaneous adsorption of two species. This method also provides the dilational rheological measurements based on low frequency harmonic drop oscillations. The tensiometric results show that the equilibrium states of the mixed βCS/DoTAB layers built up on the two different routes do not differ significantly, that is, the general compositions of the mixed layers are similar. However, the results of dilational rheology for the two adsorption strategies are remarkably different indicating different dynamic characteristics of the adsorbed layers. These findings suggest that the respective mixed layers are more proteinlike if they are formed via sequential adsorption and more surfactant-like after simultaneous adsorption. In contrast to the W/A interface, at the W/H interface proteins remain at the interface once adsorbed and cannot be displaced just by competitive adsorption of surfactants.

Effective renormalized multi-body interactions of harmonically confined ultracold neutral bosons

We calculate the renormalized effective two-, three- and four-body interactions for N neutral ultracold bosons in the ground state of an isotropic harmonic trap, assuming two-body interactions modeled with the combination of a zero-range and energy-dependent pseudopotential. We work to third-order in the scattering length at(0) defined at zero collision energy, which is necessary to obtain both the leading-order effective four-body interaction and consistently include corrections for realistic two-body interactions. The leading-order, effective three- and four-body interaction energies are and , where ω and σ(ω) are the harmonic oscillator frequency and length, respectively, and energies are in units of ℏω. The one-standard deviation error ±0.0001 for the third-order coefficient in U3(ω) is due to numerical uncertainty in estimating a slowly converging sum; the other two coefficients are either analytically or numerically exact. The effective three- and four-body interactions can play an important role in the dynamics of tightly confined and strongly correlated systems. We also performed numerical simulations for a finite-range (FR) boson–boson potential, and it was comparison to the zero-range predictions which revealed that finite-range effects must be taken into account for a realistic third-order treatment. In particular, we show that the energy-dependent pseudopotential accurately captures, through third order, the finite-range physics, and in combination with the multi-body effective interactions gives excellent agreement with the numerical simulations, validating our theoretical analysis and predictions.

Heat transfer of an oscillating cylinder in a viscous incompressible fluid flow

Unsteady flow and heat transfer of the heated cylinder with transverse and longitudinal oscillations in unbounded flow of viscous incompressible heat conducting fluid are considered. Influence of amplitude, frequency and direction of harmonic oscillations of the cylinder on the near-wake structure and heat transfer are investigated.

Quantum theory of the charge-stability diagram of semiconductor double-quantum-dot systems

We complete our recently introduced theoretical framework treating the double quantum dot system with a generalized form of Hubbard model. The effects of all quantum parameters involved in our model on the charge stability diagram are discussed in detail. A general formulation of the microscopic theory is presented, and truncating at one orbital per site, we study the implication of different choices of the model confinement potential on the Hubbard parameters as well as the charge stability diagram. We calculate the charge stability diagram keeping three orbitals per site and find that the effect of additional higher-lying orbitals on the subspace with lowest-energy orbitals only can be regarded as a small renormalization of Hubbard parameters, thereby justifying our practice of keeping only the lowest-orbital in all other calculations. The role of the harmonic oscillator frequency in the implementation of the Gaussian model potential is discussed, and the effect of an external magnetic field is identified to be similar to choosing a more localized electron wave function in microscopic calculations. The full matrix form of the Hamiltonian including all possible exchange terms, and several peculiar charge stability diagrams due to unphysical parameters are presented in the appendix, thus emphasizing the critical importance of a reliable microscopic model in obtaining the system parameters defining the Hamiltonian.

Compression of bright bound soliton trains in the Bose–Einstein condensates with exponentially time-dependent atomic scattering length in an expulsive parabolic potential

Three types of two bright bound solitons with increasing coherence are investigated in the Bose–Einstein condensates (BECs) with the exponentially time-dependent interparticle interaction in an expulsive parabolic potential. Two methods are provided with symbolic computation to improve the number of matter density peaks within the given temporal range before the collapse of the solitons under the one-dimensional approximation: (i) enhancing the axial harmonic oscillator frequency; (ii) increasing the initial coherence of the bound solitons. Compression of the three- and four-bright-bound-soliton trains is presented. Estimation of the net binding forces among the bound solitons gives an explanation for the interaction patterns if the coherence of the bound state is limited. Our investigation theoretically reveals the existence of the bright bound solitons in the BECs and analyzes their complex interactions.

The use of BDS statistics for estimating the parameters of chaotic mappings and regular signals in the presence of noise

A new method has been proposed in this paper for estimating the parameters of chaotic and regular signals by their observation against the background of white noise under conditions of the a priori uncertainty about the distribution of its values. The method is based on using the nonparametric BDS statistic revealing the sensitivity toward topological properties of the attractors of chaotic, regular and random processes that are characterized by the correlation dimension. The results of numerical simulation of the method proposed for the estimation of parameters of one-dimensional and two-dimensional chaotic mappings and also the harmonic oscillation frequency for the noise with uniform and Gaussian distribution at different levels of its intensity have been presented. This study also includes the analysis of accuracy of estimating the harmonic oscillation frequency by the proposed method and its comparison with potentially attainable values.

Beta-Blockade Restores Muscle Sympathetic Rhythmicity in Human Heart Failure

Muscle sympathetic nerve firing rate increases as chronic heart failure (CHF) progresses, yet its oscillation, particularly within the frequency range encompassing 0.13 Hz, diminishes. The current study tested the hypothesis that chronic therapy with lipophilic β-adrenoceptor antagonists augments the modulation of muscle sympathetic nerve activity variability (MSNAV) at this frequency range. In 21 CHF angiotensin converting enzyme (ACE) inhibitor-treated patients (age: 53 ± 2, ejection fraction: 20 ± 2%), MSNA was recorded before and after 4 months of β-blockade with either metoprolol (up to 50mg b.i.d.) or carvedilol (up to 25mg b.i.d.). Harmonic MSNAV was assessed by coarse graining spectral analysis. Both drugs lowered heart rate similarly (-13 ± 2 beats/min; P < 0.001) but neither affected MSNA burst frequency (-7 ± 4 bursts/min, not significant). Before β-blockade, harmonic MSNA power in the region encompassing 0.13 Hz was essentially absent. Beta-blockade increased the mean values for total power (from 0.00 to 0.50 Hz; 5.2 ± 0.8 to 6.8 ± 1.2U(2); P < 0.001) and for harmonic MSNA spectral power across the 0.1-0.22 Hz frequency range (from 0.48 ± 0.10 to 1.50 ± 0.32 U(2), F = 12.2; P < 0.001). Both carvedilol and metoprolol had a similar effect. In patients with CHF receiving ACE inhibitors, adding a β-adrenoceptor antagonist restores low and high frequency harmonic oscillations in MSNA. Beta-1 antagonism is sufficient to achieve this response. Augmented modulation of sympathetic outflow could contribute to the beneficial effects of β-blockade in CHF on sudden death and disease progression.

The New Method on Detection Singularity of Harmonics in Power System

This paper introduces a new method which can detect singularity of harmonics in power system, and combining the wavelet transform with Fourier transform to give full play their advantages, commonly detect and analyse the harmonic in power system. Firstly, using the wavelet transform to analyze the high frequency components of the signals, and determine the signal catastrophe point and occurring time and amplitude of high frequency harmonic oscillation, then analyze the low frequency component by FFT, and require the harmonics parameters. This paper gives the harmonic detection scheme which combines wavelet transform and FFT, and simulation and analysis the harmonic wave with the singular point in power system. The simulation result is satisfied and it is validated that the proposed method has the good analytical capability of unstable signals.

Transitionless quantum drivings for the harmonic oscillator

Two methods to change a quantum harmonic oscillator frequency without transitions in a finite time are described and compared. The first method, a transitionless-tracking algorithm, makes use of a generalized harmonic oscillator and a non-local potential. The second method, based on engineering an invariant of motion, only modifies the harmonic frequency in time, keeping the potential local at all times.

The action variable and frequency of a relativistic harmonic oscillator

We present three series representations of the frequency of a relativistic harmonic oscillator. The first two representations use two equivalent forms of the action variable. The third representation involves determining its period by direct integration. The energy dependance of the oscillator frequency is manifestly seen in all three representations. We demonstrate that all three forms yield the same expression for the frequency in the case of the weakly relativistic oscillator and have an identical nonrelativistic limit.

LIE SYSTEMS AND INTEGRABILITY CONDITIONS FOR t-DEPENDENT FREQUENCY HARMONIC OSCILLATORS

Time-dependent frequency harmonic oscillators (TDFHOs) are studied through the theory of Lie systems. We show that they are related to a certain kind of equation in the Lie group SL(2, ℝ). Some integrability conditions appear as conditions to be able to transform such equations into simpler ones in a very specific way. As a particular application of our results we find t-dependent constants of the motion for certain one-dimensional TDFHOs and the general solution for a two-dimensional TDFHO. Our approach provides a unifying framework which allows us to apply our developments to all Lie systems associated with equations in SL(2, ℝ) and to generalize our methods to study any Lie system.

Change in the type of bifurcation resulting in periodic oscillations in delayed feedback diode lasers

The appearance of oscillating regimes in a delayed feedback diode laser is studied analytically and numerically. Based on the Lang—Kobayashi model, the transition of the usual oscillation mechanism, related to the transition through the Hopf bifurcation, to hard excitation of the spike regime is studied. The change in the regime of the instability development has a nature of a phase transition. An explicit expression is derived for the frequency of small harmonic oscillations appearing during the transition through the Andronov—Hopf bifurcation. The boundary between two different regimes of the development of laser power oscillations is determined in the parameter space.

The absorption and spreading of aqueous finishing fluids onto textile fiber surfaces

The mechanism of ink absorption at the fiber surface, and also the penetration of ink into the fiber structure are key phenomena of textile finishing technology. To obtain high quality finishes, it is important to understand the relative importance of the parameters that define the absorption rate and spreading ratio of droplet shaped fluid elements that impact the textile surface.A simple model that combines Darcy's Law and harmonic droplet oscillator frequency forms a precursor to further advanced Dissipative Particle Dynamic (DPD) modeling. Experimental data for several combinations of textile and model fluids are presented. The key technical challenges to be addressed and overcome in the near future are discussed.

No-core shell model in an effective-field-theory framework

We present a new approach to the construction of effective interactions suitable for many-body calculations by means of the no-core shell model (NCSM). We consider an effective field theory (EFT) with only nucleon fields directly in the NCSM model spaces. In leading order, we obtain the strengths of the three contact interactions from the condition that in each model space the experimental ground-state energies of 2H, 3H and 4He be exactly reproduced. The first ( 0 + ; 0 ) excited state of 4He and the ground state of 6Li are then obtained by means of NCSM calculations in several spaces and frequencies. After we remove the harmonic-oscillator frequency dependence, we predict for 4He an energy level for the first ( 0 + ; 0 ) excited state in remarkable agreement with the experimental value. The corresponding 6Li binding energy is about 70% of the experimental value, consistent with the expansion parameter of the EFT.

Damping of a harmonic oscillator in a squeezed vacuum without rotating-wave approximation

A single harmonic oscillator interacting with a broadband squeezed reservoir is analyzed within the framework of master equation without invoking the rotating-wave approximation. The dynamical evolution and photon statistics of the system are investigated by studying mean photon number and second order intensity–intensity correlation function, respectively, under resonance condition which show transient oscillations at twice the harmonic oscillator frequency. The transient fluorescent spectrum reveals asymmetric features. Inclusion of vacuum and field-dependent frequency shifts affects the thermal equilibrium value of the average photon number of the harmonic oscillator.