Spectrum of the Relativistic Particles in Various Potentials

We extend the notion of Dirac oscillator in two dimensions, to construct a set of potentials. These potentials becomes exactly and quasi-exactly solvable potentials of non-relativistic quantum mechanics when they are transformed into a Schr\"{o}dinger-like equation. For the exactly solvable potentials, eigenvalues are calculated and eigenfunctions are given by confluent hypergeometric functions. It is shown that, our formulation also leads to the study of those potentials in the framework of the supersymmetric quantum mechanics

Calculation of the energy spectrum of a two-electron spherical quantum dot

We study the energy spectrum of the two-electron spherical parabolic quantum dot using the exact Schroedinger, the Hartree-Fock, and the Kohn-Sham equations. The results obtained by applying the shifted-1/N method are compared with those obtained by using an accurate numerical technique, showing that the relative error is reasonably small, although the first method consistently underestimates the correct values. The approximate ground-state Hartree-Fock and local-density Kohn-Sham energies, estimated using the shifted-1/N method, are compared with accurate numerical self-consistent solutions. We make some perturbative analyses of the exact energy in terms of the confinement strength, and we propose some interpolation formulae. Similar analysis is made for both mean-field approximations and interpolation formulae are also proposed for these exchange-only ground-state cases.Comment: 18 pages, LaTeX, 2 figures-ep

Energy Spectrum of a 2D Dirac Oscillator in the Presence of the Aharonov-Bohm Effect

We determine the energy spectrum and the corresponding eigenfunctions of a 2D Dirac oscillator in the presence of Aharonov-Bohm (AB) effect . It is shown that the energy spectrum depends on the spin of particle and the AB magnetic flux parameter. Finally, when the irregular solution occurs it is shown that the energy takes particular values. The nonrelativistic limit is also considered.Comment: Latex, 12 page

Influence of Gravity on noncommutative Dirac equation

In this paper, we investigate the influence of gravity and noncommutativity on Dirac equation. By adopting the tetrad formalism, we show that the modified Dirac equation keeps the same form. The only modification is in the expression of the covariant derivative. The new form of this derivative is the product of its counterpart given in curved space-time with an operator which depends on the noncommutative $\theta$-parameter. As an application, we have computed the density number of the created particles in presence of constant strong electric field in an anisotropic Bianchi universe.Comment: 9 pages, correct some miprints, Accepted for publication in journal of Mod. Phys. Letters

Solution of Massless Spin One Wave Equation in Robertson-Walker Space-time

We generalize the quantum spinor wave equation for photon into the curved space-time and discuss the solutions of this equation in Robertson-Walker space-time and compare them with the solution of the Maxwell equations in the same space-time.Comment: 16 Pages, Latex, no figures, An expanded version of paper published in International Journal of Modern Physics A, 17 (2002) 113

Computation of inflationary cosmological perturbations in chaotic inflationary scenarios using the phase-integral method

The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used for computing cosmological perturbations in the quadratic chaotic inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to fifth order of the phase-integral approximation. We show that, the phase integral gives a very good approximation for the shape of the power spectra associated with scalar and tensor perturbations as well as the spectral indices. We find that the accuracy of the phase-integral approximation compares favorably with the numerical results and those obtained using the slow-roll and uniform approximation methods.Comment: 21 pages, RevTex, to appear in Phys. Rev

On the forward cone quantization of the Dirac field in "longitudinal boost-invariant" coordinates with cylindrical symmetry

We obtain a complete set of free-field solutions of the Dirac equation in a (longitudinal) boost-invariant geometry with azimuthal symmetry and use these solutions to perform the canonical quantization of a free Dirac field of mass $M$. This coordinate system which uses the 1+1 dimensional fluid rapidity $\eta = 1/2 \ln [(t-z)/(t+z)]$ and the fluid proper time $\tau = (t^2-z^2)^{1/2}$ is relevant for understanding particle production of quarks and antiquarks following an ultrarelativistic collision of heavy ions, as it incorporates the (approximate) longitudinal "boost invariance" of the distribution of outgoing particles. We compare two approaches to solving the Dirac equation in curvilinear coordinates, one directly using Vierbeins, and one using a "diagonal" Vierbein representation

Electron-positron pair creation in the superposition of two oscillating electric field pulses with largely different frequency, duration and relative positioning

Production of electron-positron pairs in two oscillating strong electric field pulses with largely different frequencies and durations is considered. In a first scenario, the influence of a low-frequency background field on pair production by a short main pulse of high frequency is analyzed. The background field is shown to cause characteristic modifications of the momentum spectra of created particles which, in turn, may be used for imaging of the background pulse. In a second scenario, an ultrashort, relatively weak assisting pulse is superimposed onto a strong main pulse. By studying the dependence of the pair production on the field parameters it is shown that duration and relative position of the ultrashort pulse modify the momentum spectra of produced particles in a distinctive way. Both scenarios enable, moreover, to extract partial information about the time periods when pairs with certain momenta are produced predominantly.Comment: 10 pages, 9 figure

Computation of inflationary cosmological perturbations in the power-law inflationary model using the phase-integral method

The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used for computing cosmological perturbations in the power-law inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to ninth-order of the phase-integral approximation. We show that, the phase-integral approximation exactly reproduces the shape of the power spectra for scalar and tensor perturbations as well as the spectral indices. We compare the accuracy of the phase-integral approximation with the results for the power spectrum obtained with the slow-roll and uniform approximation methods.Comment: 16 pages, Revtex, to appear in Physical Review

LCC-HVDC Connection of Offshore Wind Farms With Reduced Filter Banks

Despite being more efficient, line commutated converter-HVDC links for the connection of large offshore wind farms have ac-filter bank size as one of their main drawbacks. This paper shows how the HVDC rectifier filter banks can be substantially reduced by taking advantage of the additional control possibilities offered by the use of wind turbines with fully rated converters. PSCAD simulations validate wind farm and diode rectifier HVDC link operation with a capacitor and filter bank five times smaller than its usual value. The proposed control algorithm allows for good harmonic and reactive power sharing between the different wind turbines. As the reduced capacitor bank operation leads to a redistribution of harmonic and reactive currents, an efficiency study has been carried out to evaluate the new power loss distribution with the reduced filter banks