Oscillator Potential Well Research Articles

Multiscale quantum harmonic oscillator optimization algorithm with multiple quantum perturbations for numerical optimization

Multi-scale quantum harmonic oscillator algorithm (MQHOA) is a recent proposed intelligent algorithm, in which the optimization process can be regarded as the multi-scale quantum annealing process with respect to the constraint of the harmonic oscillator potential well. It has been proved effective and efficient to deal with unimodal and multimodal numerical optimization problems. However, it takes a long time for the particles system to reach the ground-state equilibrium at each annealing scale. Motivated by this situation, a diffusion Monte Carlo method based dynamic sampling regulation strategy is proposed to enhances the sampling efficiency by dynamically adjusting the sampling frequency. Moreover, the particles with different kinetic energies are introduced into the optimization system as quantum perturbations, which reduces the probability of the algorithm falling into a local optimum by keeping the different searching scales simultaneously. The theoretical derivations of this method are presented. The effectiveness of the algorithm is studied by comparing it with previous versions of the MQHOA and several famous intelligent algorithms on uni- and multimodal benchmark functions. The experimental results illustrate that the proposed method has a comparable performance for numerical optimization problems.

On the Temperature Role in the Tunneling Process at the Low-Energy Nuclear Fusion

The temperature dependence of the coefficient of tunneling through the Coulomb barrier is estimated for nuclei of the hydrogen isotopes at comparatively low temperatures using a model of screened Coulomb interaction potential between the isotopes put inside an external oscillator potential well. The temperature dependences for the tunneling coefficient are calculated for pp-, pd-, pt-, dd-, and dt-processes at different screening radii. The probable role of pp-reactions is discussed.

Dynamic scale quantum‐inspired optimisation algorithm under harmonic oscillator potential well

A quantum-inspired optimisation algorithm with dynamic scale sampling is proposed for converging to the ground state efficiently to obtain the optimal solution. The proposed algorithm maintains diversity to discourage premature convergence through the niching method. Dynamic adjustment of sampling resolution is utilised to find a balance between exploration and exploitation. Energy level transition inside each niche and niches energy balance among niches improve the searching efficiency by guidance energy information of energy equilibrium point. The experimental results on benchmark function sets with compared algorithms show that the proposed scheme is dominant in accuracy and stability.

Measurement of gravity acceleration by cold atoms in a harmonic trap using Kapitza-Dirac pulses

The interferometry of two Kapitza-Dirac (KD) pulses acting on cold atoms in a harmonic oscillator potential well is investigated by Feynman path integral method. The wave function and density distribution function of the system at a given time are calculated analytically by using the propagator under the action of an external field. The first KD pulse acts on cold atoms to produce a large number of modes in the harmonic oscillator potential well. The maximum value of wave packet of mode 0 is larger than those of other modes. These modes evolve along different paths. The external field changes the phase of each mode and makes the evolution path of the mode deviate from that without the external field. When the second KD pulse is added, it splits the mode of the first KD pulse, and thus generates more modes. These modes will evolve along different paths under the action of external field and harmonic potential well, and interfere with each other. At the moment of measurement, all the wave packets are separated without overlapping. The effect of the external field does not change the magnitude of the density distribution at the time of measurement, but makes the wave packet of each mode shift. The phase difference between adjacent modes decreases linearly with the increase of field intensity. When the external field is a gravity field, we calculate the Fisher information and the Cramer-Rao lowér bound. The Fisher information is proportional to the mass of atoms and inversely to the third power of harmonic potential well frequency. We can improve the measurement accuracy of interferometer by reducing the frequency of harmonic potential well and increasing atomic mass. When the initial state is the ground state of the harmonic potential well, the accuracy of the gravity acceleration measured by the interference device can be obtained to be 10<sup>–9</sup> by using the experimental parameters. The initial state is the ground state of the harmonic potential well and the external field, and the calculation result indicates that the measurement accuracy will decrease. At the same time, the enhancement of inter-atomic repulsion and attraction interaction will also lead the measurement accuracy to increase.

Quantum spatial-periodic harmonic model for daily price-limited stock markets

We investigate the behaviors of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is considered to be oscillating and damping in a quantum spatial-periodic harmonic oscillator potential well. A complicated non-linear relation including inter-band positive correlation and intra-band negative correlation between the volatility and trading volume of a stock is numerically derived with the energy band structure of the model concerned. The effectiveness of price limit is re-examined, with some observed characteristics of price-limited stock markets in China studied by applying our quantum model.

BOSE–EINSTEIN CONDENSATION OF A q-DEFORMED BOSE GAS IN A RANDOM BOX

The q-deformed Bose–Einstein distribution is used to study the Bose–Einstein condensation (BEC) of a q-deformed Bose gas in random box. It is shown that the BEC transition temperature is lowered due to random boundary conditions. The effects of q-deformation on the properties of the system are also discussed. We find some properties of a q-deformed Bose gas, which are different from those of an ordinary Bose gas. Similar results are also shown for q-bosons confined in a harmonic oscillator potential well.

Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects

Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature.

Raman scattering from the peroxide ion in Cs2O2

AbstractThe Raman spectrum of Cs2O2 excited at 632.8 nm shows a single O2−2 fundamental band at wavenumber of 742.5 cm−1 and second and third overtones at 1468.5 and 2176.8 cm−1, respectively. The harmonic wavenumber ωe = 759.5 ± 0.7 cm−1 and anharmonicity constant ωexe = 8.4 ± 0.3 cm−1 were calculated directly from the measurements. These results are compared with ωe = 1151.0 ± 1.5 cm−1 and ωexe = 9.6 ± 0.5 cm−1 recently found for O2− ion in CsO2 by others. The lower ωexe of O2−2 relative to that of O2− indicates a broader (smaller curvature) anharmonic oscillator potential well. Copyright © 2002 John Wiley & Sons, Ltd.

A Note on "A Thermodynamic Analysis to Explain the Boiling-Point Isotope Effect for Molecular Hydrogen"

A simple one-dimensional harmonic oscillator potential well has been used to provide a pedagogical quantitative explanation for college chemistry students for the difference in the boiling points of the three forms of molecular hydrogen. In that scheme the energy levels have an m-1/2 dependence on the molecular mass, m. In this paper we use a more realistic potential to represent intermolecular forces, showing that there is an additional m-1 dependence on the molecular mass and that the temperature differences follow in a more direct manner.

A small particle model as a possible explanation of recently reported cavity lights

Very unusual light phenomena have been observed inside superconducting niobium cavities under an electrical excitation equivalent to an average acceleration of ∼4 MV/ m . Of particular interest is the observation of what appear to be objects executing elliptical orbits. A small particle model that yields a cylindrical harmonic oscillator potential well inside such a cavity is developed and appears to offer considerable promise as an analytical framework in which to understand these observations; the harmonic oscillator potential well has elliptical orbits as general solutions. However, explicit calculations indicate that with the cavity excitation parameters associated with this data, it is highly unlikely that a small object orbiting in such a potential well can be made of any known material. Deficiencies of the model are discussed, and avenues for further study, both theoretical and experimental, are indicated..

Shell and surface effects in the static Wigner phase-space distribution function of nuclei

Abstract Using smoothed single-particle occupation numbers, the contribution of shell and surface effects to the static Wigner phase-space distribution function for non-interacting nucleons in an external, spherical, harmonic oscillator potential well is determined. The smoothing procedure illustrates clearly the strong quantum oscillations of the distributions function around the constant value for an infinite Fermi gas, and allows the separation of the contributions arising from shell effects connected with the structure of the single-particle level spectrum near the Fermi surface, and surface effects associated with single reflections of nucleons from the surface of the potential well. The temperature dependence of these effects in the distribution function is also investigated and a thermodynamical definition of the shell contribution to the kinetic energy density is suggested.

DWBA analysis of the heavy ion induced transfer reaction

The heavy-ion induced transfer reactions have been analysed using the finite-range DWBA. The following reactions are treated for incident energies near the Coulomb barrier: 14N( 14N, 13N) 15N, 12C( 16O, 16O) 12C, 11B( 16,, 15N) 12C and 27Al( 16O, 15N) 28Si. In most cases the transfered particle is assumed to be bound in a harmonic oscillator potential well. Part of the calculations has been performed for a simple shell model with the Woods-Saxon potential. Good agreement with experiments can be obtained for reactions involving one-nucleon transfer. For the α-particle transfer process, the calculation shows complicated angular distributions, depending on various parameters.

Method for separating the relative motion of two nucleons in oscillator potential well

Invariant coefficients independent of magnetic quantum numbers are introduced for separating the relative motion of two nucleons in an oscillator potential well (“generalized Talmi coefficients”). Tables of these coefficients are given for the first oscillator states including 3p and 3f shells.

Application to Electron Scattering of Center-of-Mass Effects in the Nuclear Shell Model

The usual shell-model treatment of the nuclear scattering of high-energy electrons neglects the motion of the center of mass of the nucleus. The correction due to this is calculated for the case of an oscillator potential well and gives a simple additional factor multiplying the nuclear form factor.