Table of contents

The Wigner distribution function for the time-dependent quadratic Hamiltonian system in the coherent Schrödinger cat state is investigated. The type of state we consider is a superposition of two coherent states, which are by an angle of π out of phase with each other. The exact Wigner distribution function of the system is evaluated under a particular choice of phase, δ_{c, q}. Our development is employed for two special cases, namely, the Caldirola–Kanai oscillator and the frequency stable damped harmonic oscillator. On the basis of the diverse values of the Wigner distribution function that were plotted, we analyze the nonclassical behavior of the systems.

We studied the effects of inhomogeneous magnetic field on entanglement and teleportation in a two-qubit Heisenberg XXZ chain with intrinsic decoherence taken into account. The dependences of the entanglement and fully entangled fraction on the inhomogeneous magnetic fields b and time t are investigated in detail. The contrast between different initial states, including pure and mixed states, is presented.

Kerner and Mann's recent research on the Hawking radiation of the Rindler space-time and spherically symmetric uncharged black hole shows that the Hawking temperature can be obtained by the fermion tunneling method. In this paper, we extend Kerner and Mann's work to the axially symmetric case and study the Hawking radiation of charged fermions of the NUT Kerr–Newman black hole. As a result, the Hawking temperature is recovered, and it is exactly the same as that obtained by other methods.

Exact solutions to the time-dependent Schrödinger equation that governs the spiral motions of spinning particles are obtained, and the geometric phases that can be written as path integral of the vector potential of gravitomagnetic monopole (dual mass) are studied. Two illustrative examples of the confined spinning particles (e.g. a photon moving in a helical fiber and an electron confined by a planar radial electric field) are considered. It is shown that the confined spinning particles undergoing spiral motions seem to move inside a gravitomagnetic field produced by an equivalent gravitomagnetic monopole, i.e. the wavefunctions in the spiral motions of confined spinning particles acquire geometric phases, which are equivalent to the phase shift of a zero-spin particle that moves in the vector potential of a gravitomagnetic monopole. This means that the spiral motions of the confined spinning particles in proper potential fields can be used to simulate the gravitomagnetic vector potentials of dual mass. Though there is at present no evidence for the existence of gravitomagnetic monopole, the work presented here may stimulate interest in some areas such as the gravitationally induced quantum effects (relativistic quantum gravitational effects).

In this paper, the Exp-function method is used to find an exact solution of the equal-width wave (EW) equation. The method is straightforward and concise, and its applications are promising. It is shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving the EW equation.

The transfer of spin between atoms and a radiation field is formulated in an algebraic model. The system is composed of three-levels atoms in interaction with a radiation field. The appearance of atomic squeezing when the photon sector of the initial state consists of a squeezed photon state is analysed. It is found that atomic squeezing depends not only on the initial state but also on the interaction couplings and the number of atoms of the system.

We introduce a new class of unitary transformations based on the Lie algebra that generalizes, for certain particular representations of its generators, well-known squeezing transformations in quantum optics. To illustrate our results, we focus on the two-mode bosonic representation and show how the parametric amplifier model can be modified in order to generate such a generalized squeezing operator. Furthermore, we obtain a general expression for the bipartite Wigner function which allows us to identify two distinct sources of entanglement, here labelled dynamical and kinematical entanglement. We also establish a quantitative estimate of entanglement for bipartite systems through some basic definitions of entropy functionals in continuous phase-space representations.

In this paper, we obtain the approximate solution for the soliton solution of a new coupled modified Korteweg–de Vries (MKdV) system with initial conditions by the Adomian decomposition method (ADM) and the variational iteration method (VIM) and then numerical results from the two methods are compared, showing that the ADM leads to more accurate results. Furthermore, the VIM overcomes the difficulty arising when calculating the Adomian polynomials, which is an important advantage over the ADM. The numerical results show that only a few terms are sufficient to obtain accurate solutions.

Motivated by recent experiments on Faraday waves in Bose–Einstein condensates (BECs), we investigate the dynamics of a two-component cigar-shaped BEC subjected to periodic modulation of the strength of the transverse confinement. It is shown that two coupled Mathieu equations govern the dynamics of the system. We found that the two-component BEC in a phase mixed state is relatively more unstable towards pattern formation than the phase segregated state.

In this study, we construct the deformed form of the relativistic Duffin–Kemmer–Petiau (DKP) oscillator including a term qr³. The DKP oscillator with a deformed term becomes the radial sextic oscillator in the non-relativistic limit. The DKP sextic oscillator problem is solved numerically within the framework of the asymptotic iteration method. We present the energy eigenvalues for the ground and excited states.

From the invariance of the generalized space-time non-commutative commutation relations, local Poincaré and general coordinate transformations are derived. Moreover, a generalized Dirac equation is obtained. Applied to the de Sitter universe, it is shown that the space-time non-commutativity contributes to the particle creation process and induces a Casimir-like effect.

The signatures of rigid triaxiality in low-energy, low-spin nuclear spectra are discussed. Eight nuclei in the range of structural parameter 2.9<R_4/2<3.3 are explored to find out whether they are γ-static. Interestingly, this region is a transition path between X(5) critical point and the rigid rotor limit which is described by the confined β-soft (CBS) rotor model of Pietralla and Gorbachenko (2004 Phys. Rev. 70 011304).

Reaction cross sections are calculated using the Coulomb-modified Glauber model for deformed target nuclei. The deformed nuclear matter density of the target is expanded into multipoles of order k=0, 2, 4. The reaction cross sections for ¹²C+²⁷Al, ²⁰Ne+²⁷Al, ¹²C+⁶⁴Zn, ¹²C+⁹⁰Zr, ⁴⁰Ar+²³⁸U and ²⁰Ne+²³⁵U are studied at energy range (10–1000 MeV nucleon⁻¹). The most significant effects in the intermediate energy range are the Coulomb field and in-medium effects that modified the trajectory of the incident beams. Introducing the deformation effect beside the Coulomb field and in-medium effects improves the agreement with the experimental data and two empirical parameterizations in the case of not finding experimental data. Moreover, it is shown that the enhancement of the reaction cross sections is attributed to fixed orientation in deformed nuclei.

This study presents the calculation of strength functions for neutron–proton pair transfer on ⁸²Se, ⁹⁶Mo, ¹¹⁶Cd and ¹²⁸Te even–even nuclei. We study 1⁺ states, which are a part of the Gamow–Teller (GT) giant resonances in neighboring odd–odd nuclei, excited via the neutron–proton pair transfer on even–even parent nuclei. The main result of this work is to find these states using strength functions. Calculations have been made only in the particle–particle channel of charge-exchange spin–spin forces via the random phase approximation (RPA).

The special features of using the configuration interaction (CI) method in the case of the quasirelativistic radial orbitals (ROs) are described. The integrals composing the matrix elements of the one-electron part of the Breit–Pauli energy operator are rewritten in non-traditional forms. The correlation effects are taken into account within the CI approach on the basis of the transformed ROs (TROs) describing the virtual excitations of the electrons. The TROs with variable parameters are obtained from the RO of the investigated configuration by using the exponential transforming function. Calculations of the spectral characteristics of three ions (Ne V, Fe XXI and Xe XLIII) have been performed to demonstrate the potentiality of the new approach. The energy spectra of all three ions are presented. The lifetimes of the levels of Ne V and the transition probabilities of Fe XXI ion are also shown. All the results are compared with the experimental data and with the calculations of other authors.

The spin-dependent Hall (SDH) effect in degenerate semiconductors is investigated theoretically. Starting from a two-component drift–diffusion equation, an expression for SDH voltage (V_SDH) is derived, and drift and diffusive contributions to V_SDH are studied. For the possible enhancement of the diffusive part, degenerate and nondegenerate cases are examined. We find that due to an increase in the diffusion coefficient V_SDH increases in a degenerate semiconductor, consistent with the experimental observations. The expression for V_SDH is reduced in three limiting cases, namely diffusive, drift–diffusion crossover and drift, and is analysed. The results agree with those obtained in recent theoretical investigations.

In this work, the entropy generation due to the flow of a gravity-driven laminar viscous incompressible fluid through an inclined channel is investigated. Fully developed flow field is solved for a Newtonian fluid. Then, temperature field is represented in a purely analytical expression and subject to isothermal boundary conditions on the walls and constant rectangular temperature profile at the inlet. This analytical solution is not similar to the already existing ones in the open literature. Also, the temperature field is numerically resolved by using the method of lines with the same inlet and boundary conditions. These two solutions overlap, which indicates the correctness of both solutions. In obtaining both analytical and numerical solutions, no assumption is made on the initial transition and entrance region. It is shown that the effect of this region, which has been omitted in previous studies, is highly dominant on the overall entropy generation. Therefore, the detailed thermal analysis of the entrance section is outlined.

Because in thermo-field dynamics (TFD) the thermo-operator has a neat expression in the thermo-entangled state representation, we need to introduce the thermo-Wigner operator (THWO) in the same representation. We derive the THWO in a direct way, which brings much conveniece to calculating the Wigner functions of thermo states in TFD. We also discuss the condition for existence of a wavefunction corresponding to a given Wigner function in the context of TFD by using the explicit form of the THWO.

The stability of electrostatic waves, propagating nearly parallel to a uniform external magnetic field, is studied in a fully ionized, collisional plasma of positive and negative ions and a field-aligned current of drifting electrons. Expressions have been derived for the dispersion relation and growth rate using fluid theory and retaining the collisional and conductivity terms for the electrons. The plasma can, in general, support two modes, which have frequencies that are a composite of the ion acoustic and ion gyro frequencies. The growth rate of the modes increases with increasing drift velocities of the electrons and decreases with increasing negative ion densities.

Focusing of hot plasma flowing in a channel with a blunt object at its exit by lateral boundary injection of cold fluid is investigated numerically. A two-dimensional axisymmetric model based on one-fluid magnetohydrodynamic equations including viscous and thermal conduction effects is used. For the numerical simulation, the upwind scheme with uniform mesh in space and time is adopted. The evolution of the temperature, velocity and pressure of the plasmas in the channel is analyzed. It is found that increasing the pressure of the cold lateral flow compresses the thermal plasma flow such that the temperature profile of the hot plasma flow becomes more focused. Increasing the incident angle of the cold flow tends to increase the temperature gradient of the hot flowing plasma but tends to decrease the temperature on the surface of the object. The results are useful for controlling the temperature of channel flows as well as objects placed in them.

A study of Nb doping in lead zirconate (PbZrO₃) has been carried out by using a quantum-chemical method developed for crystals and a periodic supercell model. One of the Zr atoms was replaced by an Nb atom in the supercell consisting of 80 atoms. The obtained geometry optimization for the defective region points to defect-outward atomic movements, which are accompanied by some reduction of atomic charges. It is observed that an extra electron imposed by the Nb impurity is transferred to the conduction band of the material and contributes to the n-type electrical conductivity, explaining indirectly some of the experimental observations.

In this paper, the microscopic theory of the relative change in the velocity of sound with temperature of La_0.5Ca_0.5MnO₃ is reported. The phonon Green function is calculated using the Green function technique of Zubarev (1960 Sov. Phys.—Usp.3 320) in the limit of zero wave vector and low temperature. The electronic Hamiltonian of the lattice model in the presence of the phonon interaction with the hybridization between the conduction electrons and l-electrons is used. The relative change in the velocity of sound at various temperatures is studied for different model parameters, namely the position of the l-level, the effective phonon coupling strength, the Coulomb interaction and the hybridization strength. The phonon anomalies observed experimentally at different temperatures are explained theoretically. An abrupt change in velocity at the Neel temperature (T_N) is clearly observed. It is observed that different parameters influence the velocity of sound and the Neel temperature increases with increase in the Coulomb interaction.

Ultra-high-energy cosmic rays' (UHECR) maps at 60 EeV have been found recently by the AUGER group to be spreading anisotropy signatures in the sky. The results have been interpreted as a manifestation of AGN sources ejecting protons at GZK (Greisen–Zatsepin–Kuzmin) edges, around or below 80 Mpc distances, mostly from Supergalactic (SG) plane. The result is surprising due to the lack of correlation with the much nearer Virgo cluster. Moreover, early GZK cutoff in the spectra may be better reconciled with light nuclei (than with protons). In addition, a large group (of nearly a dozen) of events cluster suspiciously along Cen-A. Finally, proton UHECR composition nature is in sharp disagreement with the earlier AUGER claim of a heavy nuclei dominance at 40 EeV, within 13 extreme events (ln A=2.6±0.6). Therefore, we interpret here the signals as mostly UHECR light nuclei (He, Be, B, C and O) ejected from nearest Cen-A, UHECR smeared by galactic magnetic fields, whose random vertical bending is overlapping with SG arm. The (possible) AUGER misunderstanding took place because of a rare coincidence between the SG plane (arm) and the smeared (randomized) signals from Cen-A, bent orthogonally to the galactic fields. Our derivation verifies the consistency of the random smearing angles for He, Be, B, C and O range, respectively, ≳2.7°–11° in reasonable agreement with the AUGER main group event around Cen-A. Only a few other rare events are spread elsewhere. The more collimated from Cen-A, the lighter (lnA_He⩽2). The more spread, the heavier (lnA⩾2). Consequently, Cen-A is probably one of the best candidate UHE neutrinos at tens–hundreds of PeVs. This solution may be tested soon by future (and may even have already been recorded) clustering around the Cen-A barycenter, events smeared by vertical galactic magnetic forces on the lightest nuclei.

A correlative study between the intensity of a geomagnetic storm (given by the Dst index) and the peak value reached by some solar wind parameters (velocity and density) and the southward component of the interplanetary magnetic field (IMF) is made. This study has been performed by using hourly values of the Dst index and measurements taken by the ACE spacecraft in the period 2000–2005, for which 72 geomagnetic storms were considered. It is confirmed that peak Dst is correlated to the maximum negative component B_z of the IMF better than the maxima of n and V (solar wind number density and speed, respectively). By considering all the storms, the correlation coefficient was found to be 0.88. If we consider the geomagnetic storms for which - 200 nT < peak Dst < - 60 nT, a lower correlation coefficient of 0.63 is obtained.