Generalized path-integral solution and coherent states of the harmonic oscillator in D-dimensions

We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.     

A mapping-independent analysis for the spectra of the non-commutative two-dimensional harmonic oscillator

We propose a mapping-independent method to analyze the spectra of the non-commutative two-dimensional harmonic oscillator. The path integral formulation is applied and an effective Lagrangian is obtained. The spectra are read off directly and the question of uniqueness is answered.     

Radial coherent states—From the harmonic oscillator to the hydrogen atom

We construct spectrum generating algebras of SO(2, 1) ～ SU(1, 1) in arbitrary dimension for the isotropic harmonic oscillator and the Sturm-Coulomb problem in radial coordinates. Using these algebras, we construct the associated radial Barut-Girardello coherent states for the isotropic harmonic oscillator (in arbitrary dimension). We map these states into the Sturm-Coulomb radial coherent states and show that they evolve in a fictitious time parameter without dispersing.     

Dynamics of the Earth’s radiation belts

In this article, we provide a short review of the current state of the field of the radiation belts of the Earth. The main attention is given to the variations of energetic particle fluxes during geomagnetic storms. Electron and proton acceleration mechanisms in the terrestrial magnetosphere are discussed. The possibility of predicting various space weather parameters using the data on relativistic electrons of the outer radiation belt is discussed.     

Nuclei in the vicinity of ‘island of inversion’ through the fusion reaction

The level structures of N ～ 19 nuclei such as ^32,34P have been investigated using the ¹⁸O(¹⁸O,xnyp) and ¹⁸O(¹⁶O,xnyp) reactions at an incident beam energy of about 34 MeV. The de-exciting γ-transitions were recorded using an array of clover detectors. These detectors have the dual advantage of higher efficiency at E _γ ≥ 2 MeV, and are capable of providing information on the linear polarization of the observed γ-transitions. These polarization measurements when coupled with the angular correlations help us to assign uniquely the spin parity for the observed levels. The experimental results have been compared with the predictions of the spherical shell model. The shell-model calculations are able to reproduce the observed energy levels to a reasonable degree. However, the observed transition probabilities are not reproduced by the calculations. Hence there is a need to re-visit these calculations using more detailed and microscopic effective interactions.     

Performance of a quantum heat engine cycle working with harmonic oscillator systems

A cycle model of an irreversible heat engine working with harmonic systems is established in this paper. Based on the equation of motion of an operator in the Heisenberg picture and semi-group approach, the first law of thermodynamics for a harmonic system and the time evolution of the system are obtained. The general expressions for several important parameters, such as the work, efficiency, power output, and rate of entropy production are derived. By means of numerical analysis, the optimally operating regions and the optimal values of performance parameters of the cycle are determined under the condition of maximum power output. At last, some special cases, such as high temperature limit and frictionless case, are dis-cussed in brief.     

Bound states of the Klein－Gordon and Dirac equations for scalar and vector harmonic oscillator potentials

We give the exact bound states of the Klein－Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials.     

Dynamics of Bose–Einstein condensate in a harmonic potential and a Gaussian energy barrier

We have studied the dynamics of Bose–Einstein condensate by solving numerically the Gross-Pitaevskii (GP) equation. We examined the periodic behaviour of the condensate in a shifted harmonic potential, and further demonstrated the tunneling effect of a condensate through a Gaussian energy barrier, which is inserted after the condensate has been excited by shifting the harmonic trapping potential to a side. Moreover, it is shown that the initial condensate evolves dynamically into two separate moving condensates after the tunneling time under certain conditions.     

Measuring the ‘complexity’ of sound

Sounds in the natural environment form an important class of biologically relevant non-stationary signals. We propose a dynamic spectral measure to characterize the spectral dynamics of such non-stationary sound signals and classify them based on rate of change of spectral dynamics. We categorize sounds with slowly varying spectral dynamics as simple and those with rapidly changing spectral dynamics as complex. We propose rate of spectral dynamics as a possible scheme to categorize sounds in the environment.     

Quartic oscillator potential in the γ-rigid regime of the collective geometrical model

A prolate γ-rigid version of the Bohr-Mottelson Hamiltonian with a quartic anharmonic oscillator potential in β collective shape variable is used to describe the spectra for a variety of vibrational-like nuclei. Speculating the exact separation between the two Euler angles and the β variable, one arrives at a differential Schrödinger equation with a quartic anharmonic oscillator potential and a centrifugal-like barrier. The corresponding eigenvalue is approximated by an analytical formula depending only on a single parameter up to an overall scaling factor. The applicability of the model is discussed in connection to the existence interval of the free parameter, which is limited by the accuracy of the approximation, and by comparison with the predictions of the related X(3) and X(3)-β ² models. The model is applied to qualitatively describe the spectra for nine nuclei which exhibit near-vibrational features.     

Consciousness in the universe: A review of the ‘Orch OR’ theory

The nature of consciousness, the mechanism by which it occurs in the brain, and its ultimate place in the universe are unknown. We proposed in the mid 1990's that consciousness depends on biologically ‘orchestrated’ coherent quantum processes in collections of microtubules within brain neurons, that these quantum processes correlate with, and regulate, neuronal synaptic and membrane activity, and that the continuous Schrödinger evolution of each such process terminates in accordance with the specific Diósi–Penrose (DP) scheme of ‘objective reduction’ (‘OR’) of the quantum state. This orchestrated OR activity (‘Orch OR’) is taken to result in moments of conscious awareness and/or choice. The DP form of OR is related to the fundamentals of quantum mechanics and space–time geometry, so Orch OR suggests that there is a connection between the brain's biomolecular processes and the basic structure of the universe. Here we review Orch OR in light of criticisms and developments in quantum biology, neuroscience, physics and cosmology. We also introduce a novel suggestion of ‘beat frequencies’ of faster microtubule vibrations as a possible source of the observed electro-encephalographic (‘EEG’) correlates of consciousness. We conclude that consciousness plays an intrinsic role in the universe.     

‘Planetodiversity’: the variety of planets and planetary systems in the Universe

‘Planetodiversity’ is a composite word from planetary diversity. This denomination wants to parallel the common use of the term biodiversity employed in biology but translated here to the context of planetary sciences due to the proliferating variety of planets discovered outside the Solar System and theoretically proposed to exist. There are two properties that allow us a classification of a body as a planet or more generally as a ‘planetary mass object’: the orbital configuration and the physical structure (mass, energy and chemical composition). This leads respectively to the concepts that we term the ‘orbital planetodiversity’ and the ‘physical planetodiversity’. We present in a comparative way the basic planetary types observed or expected to exist within the framework of these two concepts.     

‘Quantum jumps’ observed in the fluorescence of a single ion

The laser-excited resonance fluorescence of a single Ba⁺ ion at 493 nm shows interruptions of macroscopic time durations when the ion drops into a dark state by off-resonant Raman scattering, or by weak excitation of the ²P_3/2 level. We manipulate the ion out of the state by auxiliary laser light and prove that state to be the metastable ²D_5/2 level. Fluorescence from three ions displays an enhanced rate of multiple “jumps” which reveals cooperative ionic interaction with the light.     

Improved convergence of the ‘atoms in molecules’ multipole expansion of electrostatic interaction

We study the anisotropic electrostatic interaction with high rank multipoles (? = 5) for a set of 10 van der Waals complexes and 27 DNA base pairs. Multipoles are generated by the distributed multipole analysis (DMA) and by the topological quantum theory of ‘atoms in molecules’ (AIM). The convergence of the multipolar expansion of the interaction between topological atoms is improved by distributing the moments over extra off-nuclear sites via a shifting procedure. A clear theoretical distinction is made between partitioning and distributing. A substantial improvement in the convergence of the AIM multipole expansion is observed for the smaller van der Waals molecules. An AIM representation with extra sites on the bond midpoints performs as well as DMA with just nuclear sites. However, for the larger DNA base pairs no improvement follows from the introduction of extra sites with AIM. For these larger systems AIM and DMA expansions perform equivalently, provided that now DMA allows for extra sites. This work further encourages the development of a topological intermolecular force field.     

Variants of the Nosé–Hoover oscillator

The Nosé–Hoover oscillator is a well-studied chaotic system originally proposed to model a harmonic oscillator in equilibrium with a heat bath at constant temperature. Although it is a simple three-dimensional system with five terms and two quadratic nonlinearities, it displays a rich variety of unusual dynamics, but it falls considerably short of its original purpose. This review describes two simple variants of the Nosé–Hoover oscillator, the first of which satisfies the original goal exactly, and the second of which exhibits a hidden global chaotic attractor that fills all of its three-dimensional state space.

     

Measurement of ‘closeness’ and Distinguishability of the Quantum States in Yang-Baxter Systems

Under the actions of different Hamiltonians on the different two-qubit input states by using the quantum Yang-Baxterization approach, we investigate the behaviors of the fidelity and the trace distance as measures of ‘closeness’ and distinguishability of two quantum states. The results show that the fidelity that is the main figure of merit for any communication and computing process can be kept to high values depending on the choice of the initial states and the Hamiltonians constructed by the Yang-Baxter equation. On the other hand, by choosing the initial states and Yang-Baxter systems which are the various extensions of the Yang-Baxter equations for several matrices, these quantifiers can be adjusted as desired to achieve many quantum computing and computational tasks. Furthermore, to quantify the performance of quantum teleportation we examine the teleportation fidelity for the outputs that correspond to the different two-qubit X-type states under the actions of the different Hamiltonians. It is possible to obtain high fidelity to use the quantum teleportation process.

     

Shell energy in the heaviest nuclei using the Green’s function oscillator expansion method

The Greens function oscillator expansion method and the generalized Strutinsky smoothing procedure are applied to shell corrections in the heaviest elements. A macroscopic-microscopic method with a finite deformed Woods-Saxon potential is used. The stability condition for the shell correction is discussed in detail and the parameters defining the smoothing procedure are carefully determined. It is demonstrated that the spurious contribution to the total binding energy due to the unphysical particle gas that appears in the standard method can be as large as 1.5 MeV for weakly bound neutron-rich superheavy nuclei, but the effect on energy differences (e.g., alpha-decay values) is fairly small.