Volume 6, Issue 1

The Pareto probability distribution is widely applied in different fields such us finance, physics, hydrology, geology and astronomy. This note deals with an application of the Pareto distribution to astrophysics and more precisely to the statistical analysis of masses of stars and of diameters of asteroids. In particular a comparison between the usual Pareto distribution and its truncated version is presented. Finally, a possible physical mechanism that produces Pareto tails for the distribution of the masses of stars is presented.

The reflection coefficient of bulk spin waves from a ferromagnetic multilayer with periodically modulated parameters of the exchange interaction, the uniaxial magnetic anisotropy and the saturation magnetization (a magnonic crystal) is calculated. The dependence of the reflection coefficient upon the spin wave frequency and the values of the bias magnetic field, the parameter of interfacial coupling, and the internal structure of the unit cell are investigated.

We demonstrate rather interesting manifestations of co-existence of resonance features in characteristics of the photoionization of 3d-electrons in Xe, Cs and Ba endohedral atoms. It is shown that for all of the considered atoms the reflection by the fullerene shell of photoelectrons produced by the 3d subshell photoionization affects greatly partial photoionization cross-sections of 3d 5/2 and 3d 3/2 levels and respective angular anisotropy parameters, both dipole and non-dipole adding to all of them additional maximums and minimums. The results obtained demonstrate distinctive differences between the three atoms. The calculations are performed treating the 3/2 and 5/2 electrons as electrons of different kinds with their spins “up” and “down”. The effect of the C60 shell is accounted for in the frame of the “orange” skin potential model. It is essential that in the considered photon frequency region the presented resonance features are not affected by the C60polarization.

We investigate the Bloch and dipole oscillations of a Bose Einstein condensate (BEC) in an optical superlattice. We show that, as the effective mass increases in an optical superlattice, the BEC is localized in accordance with recent experimental observations [J.E. Lye et. al. Phys. Rev. A 75, 061603 (2007)]. In addition, we find that the secondary optical lattice is a useful additional tool to manipulate the dynamics of the atoms.

An improved Monte Carlo diffusion model is used to calculate the ground state energies and chemical potentials of parahydrogen clusters of three to forty molecules, using two different p-H2-p-H2 interactions. The improvement is due to three-body correlations in the importance sampling, to the time step adjustment and to a better estimation of statistical errors. In contrast to path-integral Monte Carlo results, this method predicts no magic clusters other than that with thirteen molecules.

Presence of feedback mechanisms, both positive and negative, in the gene regulation systems is generally appreciated. The present study proposes a diagrammatic representation of these phenomena that affords their exact formulation and reveals some new facts. Topology of feedback relationships is defined by diagram configuration and quantitative evaluation is afforded by analytical apparatus coming with the diagrams. In particular, criterion for occurrence of bistability and synergy of positive and negative feedback are described in exact manner using the concept of transmission functions associated with diagram edges. The approach is demonstrated on genetic regulatory system comprising two genes whose transcription is controlled by activator and repressor proteins mutually competing for binding to the same responsive element of the DNA.

This paper investigates analytically the molecular-motor-assisted transport between the cell nucleus and cell membrane in an elongated cell, which allows the formulation of governing equations in a cylindrical coordinate system. This problem is relevant to biomimetic transport systems as well as to many biological processes occurring in living cells, such as the viral infection of a cell. The obtained analytical solution is shown to agree well with a high-accuracy numerical solution of the same problem. The developed analytical technique extends the applicability of the generalized Fourier series method to a new type of problems involving intracellular transport of organelles.

This work is devoted to the calculation of the concentration of radiation displacement defects (RDD) in bismuth germanate and bismuth silicate crystals as a function of particle energy (electrons and neutrons). Energy dependencies of RDD concentrations are discussed in comparison with results for other complex oxide crystals. The obtained results show that for the case of electron irradiation the radiation hardness of BSO and BGO should be similar to other oxide crystals, but for neutrons is drastically smaller. Additionally, for the neutron irradiation, the efficiency of the production of defects in the oxide sublattice is drastically smaller than for other oxide crystals.

We report on the fabrication of all transparent heterojunction thin film diodes of the form glass/n-ZnO: Al/p-CuAlO2 produced by a combinatorial chemical and physical technique and on a study of their electro-optical properties. The n-ZnO: Al layer was deposited by a sol-gel-dip-coating process whereas the p-CuAlO2 layer was deposited by direct current sputtering techniques. The diode structure, with a total thickness of 1100 nm showed around 60% transmittance in the visible region. The current-voltage characteristics of the device showed a rectifying nature, with a low turn-on voltage around 0.8 V, having a rectification ratio > 50 at ± 2 V. The low turn-on voltage and moderate visible transmittance of the transparent diode indicate its potential application in the field of “Transparent” or “Invisible Electronics”.

The electronic structure, linear, and non-linear optical properties of ferroelectric-semiconductor SbSBr are investigated in the non-polar (paraelectric) and polar (ferroelectric) phase, using the density functional methods in the generalized gradient approximation. The electronic band structure obtained shows that SbSBr has an indirect forbidden gap of 2.16 and 2.21 eV in the paraelectric and ferroelectric phase, respectively. The linear photon-energy dependent dielectric functions and some optical functions, such as absorption and extinction coefficients, refractive index, energy-loss function, reflectivity, and optical conductivity in both phases and photon-energy dependent second-order susceptibilities in the ferroelectric phase are calculated. Moreover, some important optical parameters, such as the effective number of valence electrons and the effective optical dielectric constant, are calculated in both phases.

We have studied the effect of the ratio of different rare-earth element on the superconducting properties and phase formation of (Nd0.33Eu0.08Gd0.58)Ba2Cu3Oz ceramic. Bulk NEG samples were prepared using the solid-state reaction process. The superconducting transition for Nd0.33Eu0.08Gd0.58Ba2Cu3Oz is T c ≈90 K and the value of the critical current density (J c) is 13.9 A/cm2 at 77 K under zero magnetic fields. This value is twice as high when compared with the (J c) value of YBCO systems (J c = 7.31 A/cm2). The obtained bulk sample was used for the production of superconducting Ag-sheathed tapes by OPIT method including hot rolling. The critical current density of the obtained tape (337 A/cm2) is one order higher than the one of the bulk sample.

The spherically symmetric vacuum metric in the relativistic theory of gravity is analyzed numerically. It is found that there is no deviation of the numerical solution from that of general relativity except in the near-horizon range. The solution obtained has the well-established analytical asymptotics for both the near-and far-horizon limits. It satisfies the causality principle and does not impose a lower limit on the graviton mass.

The method of “reverse engineering” for designing potentials in cosmologies with “quintessence” scalar field is systematically used for several types of cosmologies (through the time behavior of the scale factor). The general recipe is introduced and then applied when matter other than the scalar field is present, and for tachyonic scalar fields. The possibility of using this method for prescribing initial data in numerical simulations in cosmology is investigated.

The problem of a shallow donor impurity located at the centre of a symmetrical paraboloidal quantum dot (SPQD) is solved exactly. The Schrödinger equation is separated in the paraboloidal coordinate system. Three different cases are discussed for the radial-like equations. For a bound donor, the energy is negative and the solutions are described by Whittaker functions. For a non-bound donor, the energy is positive and the solutions become coulomb wave functions. In the last case, the energy is equal to zero and the solutions reduce to Bessel functions. Using the boundary conditions at the dot surfaces, the variations of the donor kinetic and potential energies versus the size of the dot are obtained. The problem of a shallow donor impurity in a Hemiparaboloidal Quantum dot (HPQD) is also studied. It is shown that the wave functions of a HPQD are specific linear combinations of those of a SPQD.

This paper deals with quantum mechanical interaction of no 3− with (5,5) and (8,0) swcnts. To perform this we have made an ab initio calculation based on the density functional theory. In these framework the electronic density plays a central role and it was obtained of a self-consistent field form. It was observed through binding energy that NO3− molecule interacts with each nanotube in a physisorption regime. We propose these swcnts as a potential filter device due to reasonable interaction with NO3− molecule. Besides this type of filter could be reusable, therefore after the filtering, the swcnts could be separated from NO3− molecule.

ZnO:Mn semiconductor quantum dots were prepared by solution casting led microemulsion route. Quantum dots of average size ∼2 nm were noticed in transmission electron micrographs. The present work highlights colour change phenomena (photochromic effect) of quantum dots while subjected to photon illumination. The magneto-optic measurements e.g. magnetic field (H) vs angle of rotation (θ) show step like behavior and is ascribed to the quantum confinement effect of diluted magnetic ZnO:Mn nanostructures. Further, underlying mechanism responsible for exhibiting photochromism and magneto-optic effects are also discussed.

We test the stability of the mean field solution in the Nambu-Jona-Lasinio model in a semi-quantitative manner. For stable solutions with respect to both the σ and π directions, we investigate effects of the mesonic loop corrections of 1/N c, which correspond to the next-to-leading order in the 1/N c expansion, on the high density chiral phase transition. The corrections weaken the first order phase transition and shift the critical chemical potential to a lower value. At N c = 3, however, instability of the mean field effective potential prevents us from determining the minimum of the corrected one.

The particle tunneling through a 3-D rectangular potential barrier has been studied. The simplest model for multiple internal reflections has been assumed. The explicit expression for all the transmission and reflection probability amplitudes have been derived, as well as the tunneling and reflection phase times.

Any unitary operation in quantum information processing can be implemented via a sequence of simpler steps — quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, searching for a short sequence of gates — efficient quantum circuit for a given operation, is an important task. We contribute to this issue by proposing optimization of the well-known universal procedure proposed by Barenco et al. [Phys. Rev. A 52, 3457 (1995)]. We also created a computer program which realizes both Barenco’s decomposition and the proposed optimization. Furthermore, our optimization can be applied to any quantum circuit containing generalized Toffoli gates, including basic quantum gate circuits.

An effective Hamiltonian for the generalized harmonic oscillator is determined by using squeezed state wavefunctions. The equations of motion over an extended phase space are determined and then solved perturbatively for a specific choice of the oscillator parameters. These results are used to calculate the dynamic and geometric phases for the generalized oscillator with this choice of parameters.

The Klein-Gordon equation in D-dimensions for a recently proposed ring-shaped Kratzer potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the non-central equal scalar and vector potentials. The results obtained in this work are more general and can be reduced to the standard forms in three dimensions given by other works.

We establish the supersymmetry formalism for time-dependent Schrödinger equations with effective mass and show that the corresponding supersymmetric transformations are equivalent to effective mass Darboux transformations

We carry out a systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. The major technical tools are the information theory methods and inequalities satisfied by Fisher and Shannon information measures. We focus on the compatibility of these inequalities with the prescribed (deterministic, random or quantum) temporal behavior of pertinent probability densities.

Quantum mechanical analysis of a rigid rod with one end fixed to a flat table is presented. Assuming that the rod is initally in the upright orientation, “the time of fall” is calculated using WKB wavefunctions representing energy eigenstates near the barrier summit.

In this paper we re-investigate the core of Schrödinger’s “cat paradox”. We argue that one has to distinguish clearly between superpositions of macroscopic cat states |☺〉 + |☹〉 and superpositions of entangled states |☺, ↑〉 + |☹, ↓〉 which comprise both the state of the cat (☺=alive, ☹=dead) and the radioactive substance (↑=not decayed, ↓=decayed). It is shown, that in the case of the cat experiment recourse to decoherence or other mechanisms is not necessary in order to explain the absence of macroscopic superpositions. Additionally, we present modified versions of two quantum optical experiments as experimenta crucis. Applied rigorously, quantum mechanical formalism reduces the problem to a mere pseudo-paradox.