Table of contents

The spectral properties of Ca 4pnd (J = 3) autoionizing states have been studied by employing the combination of multichannel quantum defect theory (MQDT) with the K-matrix method. The cross section of 4p_3/215d excited from 4s15d and energy levels of 4pnd (J = 3) are calculated by using a theoretical model with more complete channels, and the configuration interaction is analysed in detail between 4p_1/2nd, 4p_3/2nd_3/2,5/2 and 4p_1/2,3/2ng of five Rydberg series.

Transient free convective boundary layer flow of micropolar fluids past an impulsively started infinite vertical plate is investigated. The transformed dimensionless governing equations for the flow, microrotation and heat transfer characteristics are solved by using the Laplace transform technique. In particular, the relevant solution of the coupled governing equations was found with the second kind of the Volterra integral equation. The obtained results concerning velocity, microrotation and temperature across the boundary layer are illustrated graphically for different values of the parameters entering into the problem under consideration and the dependence of the flow and temperature fields from these parameters is discussed.

Aharonov–Anandan (AA) phases for two coupled spins in a rotating magnetic field are obtained. The conditions for the adiabatic limit are also derived. It is found that if the rotating field is confined to a plane and the total spin is an integer, the adiabatic phase or the Berry phase will be zero, but the AA phase will not. Unlike adiabatic evolution, the AA phase is not the sum of geometric phases for the subsystems.

The Hartman effect for a tunnelling particle implies that group delay time is independent of the opaque barrier width. In the present study, the tunnelling delay time in the transmission mode is studied taking into account the real band structure of an InSb-type semiconductor quantum ring and compared with that of a parabolic band structure. The system considered in this study consists of a circular loop in the presence of Aharonov–Bohm flux. It is shown that while tunnelling through an opaque barrier, the group delay time for a given incident energy becomes independent of the barrier thickness as well as the magnitude of the flux.

The impurity displacements and the g factors g_∥ and g_⊥ of the two tetragonal Ni³⁺ centres (I and II) in SrTiO₃ are theoretically investigated by using the perturbation formulae of the g factors for a 3d⁷ ion with low spin (S=1/2) in tetragonally distorted octahedra. In these formulae, the contributions to the g factors from the tetragonal distortion, the ligand spin–orbit coupling coefficient, and the ligand orbitals, which were usually neglected in previous studies (Muller K A et al 1969 Phys. Rev. B 186 361; Lacroix R et al 1964 Helv. Phys. Acta37 627), are taken into account based on the cluster approach. Centre I (or II) was ascribed to the substitutional Ni³⁺ at the Ti⁴⁺ site, associated with the nearest neighbour oxygen vacancy V_O (or the near neutral V_O−(−2e)) along the C₄ axis as a compensator. The impurity Ni³⁺ is found to shift away from (or towards) the compensator by about 0.033 nm (or 0.010 nm) along the C₄ axis, respectively. As a result, the ligand octahedron around the impurity is elongated (compressed) in centre I (II), corresponding to the negative (positive) anisotropy Δg (=g_∥−g_⊥). The theoretical g factors based on the above impurity displacements show good agreement with the observed values.

The radial parts of the Dirac equation between the inner and the outer horizon in Schwarzschild–de Sitter geometry are solved. Two limiting cases are concerned. The first case is when the two horizons are far apart and the second case is when the horizons are close to each other. In each case, a 'tangent' approximation is used to replace the modified 'tortoise' coordinate r_*, which leads to a simple analytically invertible relation between r_* and the radius r. The potential V(r_*) is replaced by a collection of step functions in sequence. Then the solutions of the wave equation as well as the reflection and transmission coefficients are computed by a quantum mechanical method.

Both dark and bright solitons are constructed exactly for a Bose–Einstein condensation with a time-dependent scattering length in an expulsive parabolic potential. It is shown analytically how the size of the cloud and the sharp peak of the condensate changes via the Feshbach resonance. It is also found that the atom loss due to three-body recombination can be controlled with the help of Feshbach resonance. The exact calculation is performed to compare the rate of the atom loss between the system with time-dependent scattering length in an expulsive parabolic potential and the system with constant scattering length.

It is shown that the energy of a mode of a classical chaotic field, following the continuous exponential distribution as a classical random variable, can be uniquely decomposed into a sum of its fractional part and of its integer part. The integer part is a discrete random variable (we call it the Planck variable) whose distribution is just the Bose distribution yielding Planck's law of black-body radiation. The fractional part is the 'dark part' represented by the 'dark variable' with a continuous distribution, which is, of course, not observed in the experiments. It is proved that the Bose distribution is infinitely divisible, and the irreducible decomposition of it is given. This means that the Planck variable can be decomposed into an infinite sum of independent binary random variables representing the 'binary photons' (more accurately photo-molecules or photo-multiplets) of energies 2^shν with s=0, 1, 2, .... These binary photons follow Fermi statistics. According to our present analysis, the black-body radiation can be viewed as a mixture of statistically and thermodynamically independent fermion gases consisting of 'binary photons'. The binary photons give a natural tool for the dyadic expansion of arbitrary (but not coherent) ordinary photon excitations. It is shown that the binary photons have wave–particle fluctuations of fermions. These fluctuations combine to give the wave–particle fluctuations of the original bosonic photons, expressed by Einstein's fluctuation formula.

The Klein–Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, V_v=V_s+constant. These isospectral problems are solved in the case of squared trigonometric potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfunctions are discussed in some detail. It is revealed that a spin-0 particle is better localized than a spin-1/2 particle when they have the same mass and are subjected to the same potentials.

A model of crystalline acetanilide, ACN accounting for the C=O and N–H vibrational self-trappings is presented. We develop a fully discrete version of ACN. We show that ACN can be described by a set of two coupled discrete nonlinear Schrödinger (DNLS) equations. Modulational instabilities (MI) are studied both theoretically and numerically. Dispersion laws for the wavenumbers and frequencies of the linear modulation waves are determined. We also derived the criterion for the existence of MI. Numerical simulations are carried out for a variety of selected wave amplitudes in the unstable zone. It is shown that instabilities grow as the wavenumbers and amplitudes of the modulated waves increase. MI grow faster in the N–H mode than in the C=O mode. Temporal evolution of the density probabilities of the vibrational excitons are obtained by the numerical integration of the coupled DNLS equations governing the ACN molecule. These investigations confirm the generation of localized modes by the phenomenon of MI and the predominance of the N–H vibrational mode in the MI process of the ACN.

Dynamical systems described by the modified quintic complex Ginzburg Landau equation and its derivative forms are considered and the stability of their bright soliton solution is investigated numerically by means of the split-step Fourier method. Some discussions related to the way of ensuring the stability of this solution are presented.

There is a widespread belief in the quantum physical community, and textbooks used to teach quantum mechanics, that it is a difficult task to apply the time evolution operator on an initial wavefunction. Because the Hamiltonian operator is, generally, the sum of two operators, then it is not possible to apply the time evolution operator on an initial wavefunction ψ(x, 0), for it implies using terms like . A possible solution is to factorize the time evolution operator and then apply successively the individual exponential operator on the initial wavefunction. However, the exponential operator does not directly factorize, i.e. . In this study we present a useful procedure for factorizing the time evolution operator when the argument of the exponential is a sum of two operators, which obey specific commutation relations. Then, we apply the exponential operator as an evolution operator for the case of elementary unidimensional potentials, like a particle subject to a constant force and a harmonic oscillator. Also, we discuss an apparent paradox concerning the time evolution operator and non-spreading wave packets addressed previously in the literature.

The nonlinear Thomson backscattering in a circularly polarized Gaussian laser pulse is investigated and spectral characteristics of the emission are discussed. It is indicated that the frequency of the emitted light is up-shifted by the nonlinear doppler effect. By using a properly focused laser beam or putting the electron before the focus, the variety of the nonlinear Doppler shift during the interaction can be minimized and quasimonochromatic x-rays are generated. Taking into account the emission power, the optimum situations for generating quasimonochromatic x-rays are explored.

The interactions between dromions have still not yet been understood very well. In this short paper, two new types of dromion interactions, dromion reflection and reconnection, are reported for the generalized Broer–Kaup system as a representative example. Dromion reflection is when a dromion behaves like a ball reflected by a wall. Essentially, it is a dromion interacting with an invisible ghost wall caused by a ghost line soliton. While dromion reconnection interaction is the scenario where the bounded dromions may be opened and then reconnected during the interaction. These two novel interaction phenomena are quite universal in high dimensions.

We consider quasi-free electrons, moving in a two-dimensional lattice, and interacting with a strong monochromatic electromagnetic field; the interaction between each electron and the lattice is considered to be sufficiently weak, so it is possible to treat it as a small perturbation. Using a variant of the stationary perturbation theory in the extended Hilbert space, we have obtained the quasi-energies and the reduced Floquet eigenvectors of a quasi-free electron. The low order perturbation corrections show that the quasi-energy spectra have positive and negative jumps and the Floquet eigenfunctions have generalized Bloch form. These results show some similarities to the corresponding properties of the conservative quasi-free electron model, in the absence of the external radiation field.

The resonant interaction between three waves in a uniform magnetized plasma is considered. Starting from the general formulae containing the coupling coefficients in implicit form, we are able to present the explicit expressions for the three-wave coupling coefficients of a warm multicomponent plasma.

The direct current electrical conductivity of ternary 40TeO₂–(60−x)V₂O₅–xMoO₃ glasses prepared by press-melt quenching technique was studied at temperatures between 90 and 403 K. From the conductivity–temperature relation, it was found that the small polaron hopping (SPH) model was applicable at the temperature above Θ _D/2 (Θ _D: the Debye temperature), and the electrical conduction was due to the non-adiabatic SPH of electrons between vanadium ions for all glasses. The hopping carrier mobility and carrier density were determined at different temperatures. At temperatures lower than Θ _D/2, a T^−1/4 dependence of the conductivity was found, which can be described by the variable-range hopping (VRH) conduction mechanism. The density of states at (or near) the Fermi level, N(E_F), was found from Mott parameters analysis, which was a function of V₂O₅ content. All the semiconducting glass compositions exhibited a crossover from VRH to SPH conduction at a characteristic temperature

An irreversible cycle model of a quantum heat engine with internal friction is established, which is composed of two adiabatic and two isomagnetic field processes. The working substance of the cycle consists of an ensemble of many non-interacting spin-1/2 systems. Based on a quantum master equation and semi-group approach, the general performance characteristics of the heat engine are investigated. The general expressions for several important parameters, such as the efficiency, power output, and rate of the entropy production, are derived. The performance of the cycle is optimized with respect to the temperatures of the working substance. By numerical solutions, the maximum power output and the corresponding parameters are calculated. The optimal regions of efficiency, temperatures of the working substance, and cycle period are determined. Moreover, the performance of the heat engine in the frictionless case is obtained, which is different from that in the friction case. Finally, the results obtained are generalized to the performance optimization of the heat engine working with spin-J systems.

Regarding a recent paper (Bruce S 2006 Phys. Scr. 74 371), we comment on cold neutron confining in a system consisting of an Aharonov–Casher together with a properly set Aharonov–Bohm configuration. We find that, for the supersymmetric ground state, an extra spin–orbit (spin-electromagnetic angular momentum density) term should be present. This effect turns out to modify the phenomenology associated with the anomalous magnetic moment of the neutron.