Table of contents

Based on the electron interference resulting from the electrons reflected at the interfaces of superlattices, the transmission coefficient of electrons passing over barriers of superlattices is discussed. For electrons occupying states above barriers, if these electrons have transmission coefficient of T⩾0.5 passing over the barriers of superlattice, the states above the barriers are defined as the conduction states, and if T<0.5, they are defined as the local states. All these conduction-states above the barriers compose a series of micro-bands, which are separated by the micro-bands composed of the local states. The width of the conduction-micro-bands is related to the barrier width and electron reflectivity at the interface of the well/barrier. For a fixed barrier width, as the electron reflectivity at interfaces increases, the conduction-micro-band width becomes narrower. The calculated energy spacing between an energy level where electrons have a maximum of transmission coefficient over the barriers and the next level where electrons have a minimum of transmission coefficient is in good agreement with measured data.

In this paper the Galitskii–Migdal–Feynman (GMF) formalism is applied to spin-polarized ³He–HeII mixtures with special emphasis on the effect of the magnetic field on hole–hole scattering. For comparison purposes, the relative phase shifts for S- and P-waves, in both GMF and Brueckner–Bethe–Goldstone (BBG) formalisms, are calculated and analysed. Also, the corresponding scattering lengths are evaluated. In polarized mixtures, the S-wave pairing decreases because of the flip of one spin in the pair; whereas the magnetic field has no effect on P-wave pairing.

The Feshbach–Villars equation (FV_1/2) is studied by comparing it with the Dirac equation and by examining its behaviour in the creation process of pairs of particles from vacuum while being perturbed by an external field using two approaches: (i) the effective action method of Schwinger and (ii) the Bogoliubov transformation. In the first approach, the transition vacuum–vacuum amplitude is determined by treating the FV_1/2 field as a fermionic field. In the second approach, the anticommutation relations are used contrary to the case of spin 0, in order to obtain meaningful probabilities. The two approaches show that the expressions of pair creation probability as well as those relating to the vacuum remaining vacuum are exactly similar to those obtained by either FV_1/2 or Dirac equations.

The effects of magnetic field strength on the backward branch of a surface ion-cyclotron wave are investigated in a semi-bounded magnetized plasma. The dispersion relation of the backward mode of the surface ion-cyclotron wave is obtained by the plasma dielectric function with the specular reflection boundary condition. The result shows the existence of the long wavelength backward mode in the surface ion-cyclotron wave. The frequency of the wave is found to be decreased with increasing wavenumber. It is also found that the wave frequency increases with an increase in the ratio of the electron gyrofrequency to the electron plasma frequency, i.e., with increasing the magnetic field strength. In addition, the group velocity of the surface ion-cyclotron wave decreases with decreasing the magnetic field strength.

A numerical study is carried out on the dynamics of a non-autonomous chaotic circuit. The parametrical dependencies and features of a time-dependent circuit are explored. A novel feature of the present circuit model is that it contains a new non-autonomous nonlinear sub-circuit, namely, a non-autonomous Chua's diode (NCD), which indicates nonlinear resistor behaviour and enhances the complexity of the standard Chua's diode. Periodic cases are observed as functions of voltage f, driving frequency ω and the frequency of NCD ϕ. Chaos occurs for appropriate system parameters.

In this paper, the method of internal resonances in a system of rods under vertical kinematic biharmonic excitation is presented. The elements of the system are connected with articulated joints. The couplings of the elements of the system through internal longitudinal forces, which are parametrical, are taken into account. The analysis of such objects under kinematic excitation may have essential significance in the study of paraseismic phenomena. The fundamental problem is to choose the appropriate model of the described object (structures, buildings, mechanical devices and mechanisms). The model includes some important properties of the object in the particular situation. The autoparametric phenomena can play an essential role in the processes of destruction of described objects. The equations of motion are obtained from Lagrange's equations and the harmonic balance method is applied. Nonlinear terms appear in the equations of motion. These terms are nonlinear damping and nonlinear inertia and have a geometric nature. The amplitudes of the vibrations in the stationary states of internal resonance are investigated. Plots of the amplitudes against frequency are presented.

An analytical investigation of the nonlinear vibration of a post-buckled beam subjected to harmonic excitations is presented. The system can be modelled as a nonlinear oscillator with parametric and external excitations having frequencies Ω ₁ and Ω ₂. The method of multiple scales is used to determine to second order the amplitude and phase-modulation equations. Attention is focused on subharmonic resonances (Ω ₁ ≅ 2ω ₀, Ω ₂ ≅ 2Ω ₀ ; Ω ₁ ≅ 3ω ₀, Ω ₂ ≅ 3ω ₀ ; Ω ₁ ≅ 4ω ₀, Ω ₂ ≅ 4ω ₀ ; Ω ₁ ≅ 5ω ₀ and Ω ₁ ≅ 6ω ₀) where ω ₀ is the natural frequency. Steady-state amplitude for each case is plotted as a function of a detuning parameter showing the influences of the several parameters. Stability is performed on figures by solid and broken lines. There exist multivalued solutions which increase or decrease by the variation of some parameters. The response amplitude is not affected by increasing and decreasing the parameters F₁ and α ₃ for the cases of subharmonics of order one-half and one-third. The solution loses stability on increasing the parameters α ₄, α ₅ and F₁ in the case of subharmonic resonance of order one-fifth and also for decreasing the parameters μ and α ₄ in the case of subharmonic resonance of order one-sixth.

The plasma–maser, an interesting nonlinear process in plasmas, is an effective means of energy up-conversion in frequency from low-frequency turbulence to a high-frequency wave. A theoretical study is made of the amplification mechanism of an electrostatic Bernstein mode wave in presence of Langmuir wave turbulence in a magnetized inhomogeneous plasma on the basis of a plasma–maser interaction. It is shown that a test high-frequency electrostatic Bernstein mode wave is unstable in the presence of low-frequency Langmuir wave turbulence. The growth rate of a test high-frequency Bernstein mode wave is calculated with the involvement of a spatial density gradient parameter. A comparative study on the role of density gradient in the generation of the Bernstein mode on the basis of the plasma–maser effect is presented.

The master equation approach, which has traditionally been used for the calculation of neutron fluctuations in multiplying systems with constant parameters, is extended to a case when the parameters of the system change randomly in time. A forward type master equation is considered for the case of a multiplying system whose properties jump randomly between two discrete states, both with and without a stationary external source. The first two factorial moments are calculated, including the covariance. This model can be considered as the unification of stochastic methods that were used either in a constant multiplying medium via the master equation technique, or in a fluctuating medium via the Langevin technique. The results obtained show a much richer characteristic of the zero power noise than that in constant systems. The results are relevant in medium power subcritical nuclear systems where the zero power noise is still significant, but they also have a bearing on all types of branching processes, such as evolution of biological systems, spreading of epidemics etc, which are set in a time-varying environment.

Supersymmetric quantum mechanics (SUSY QM) is used to determine the class of potentials that are solvable as well as to find their isospectral partners. To do that SUSY QM assumes the knowledge of the Witten superpotential as a particular solution of the Riccati equation involved in order to obtain the corresponding generalizations. Consequently, due to the fact that in statistical mechanics the internal energy is indeed known as a single temperature derivative of the Helmholtz free energy, a simple transformation has been proposed here in order to get, in an heuristic way, a Schrödinger-like thermodynamic (SLT) equation. In this proposal, the quantum Witten superpotential and the wavefunction correspond, in statistical physics, to the internal energy and to the canonical partition function respectively. With that, it is shown how all the results from SUSY QM can be incorporated in the statistical case, to find the generalized internal energy and partition functions as well as to generalize all the other related thermodynamical properties. As an example of the usefulness of the proposed SLT equation, the case of Boltzmann statistics has been considered explicitly and it was found that the corresponding generalized internal energy contain, as a particular case, the Bose–Einstein or the Fermi–Dirac probability distributions.

The damping rate γ_t(p) of on-shell transverse gluons with ultrasoft momentum p is obtained in the context of next-to-leading-order hard-thermal-loop-summed perturbation of high-temperature massless quantum chromodynamics (QCD). It is obtained in an expansion to the second order in p. The first coefficient known in the literature is recovered, but that of order p² is found to be divergent in the infrared. Divergences from light-like momenta do also occur but are circumvented. By carrying out similar calculations in the context of scalar quantum electrodynamics, it is shown that early and late external-momentum expansions yield identical results.

A numerical simulation based on full-potential linearized augmented plane wave calculations is applied to study the lattice parameters and the band-gap energy of the zincblende Al_xGa_1−xIn_1−x−yN quaternary alloys. The results obtained are in a good agreement with experimental and theoretical values.

The design and emission parameters of a spontaneous radiation source (excilamp) at a 222 nm wavelength are presented. To obtain a high-power UV radiation, a volume transverse discharge was used in the high-pressure Ne–Kr–HCl mixture. A radiation power density of 1 kW cm⁻² was gained at the excilamp output at a 2 mJ pulse energy. Successful attempts were made to synchronize the excilamp pulse with the pulse of second laser source. An optical system was developed to deliver and concentrate the UV radiation on to the area with a specified geometry. The method of modelling and analysis technique of the optical system using the OptiCAD 9.3 Optical Analysis Program software is described, as well.

The inverted harmonic oscillator problem is investigated quantum mechanically. The exact wavefunction for the confined inverted oscillator is obtained and it is shown that the associated energy eigenvalues are discrete, and the energy is given as a linear function of the quantum number n.

In Dirac's hole theory (HT), the vacuum state is generally believed to be the state of minimum energy. It will be shown that this is not, in fact, the case and that there must exist states in HT with less energy than the vacuum state. It will be shown that energy can be extracted from the HT vacuum state through application of an electric field.

We apply a numerical simulation method to study a normalized correlation function C(t) of a bistable system driven by cross-correlated noises. Based on a stochastic equivalent rule, we get a stochastic equivalent Stratonovich stochastic differential equation driven by Gaussian white noise for a bistable system driven by cross-correlated noises. Making use of a differential equation, C(t) was calculated by the numerical simulation procedure. Comparing C(t) calculated by the projection operator method of theoretics approximation to C(t) by the numerical simulation procedure, we find: (i) the difference in C(t) between the result of the theoretics approximation and that of the numerical simulation procedure is very small, i.e. the two results are approximately consistent; (ii) there is no difference in C(t) between the result of the theoretics approximation and the result of the numerical simulation procedure when the decay time t is large, i.e. they are entirely consistent; (iii) when the projection operator method is used to calculate C(t), the effects of higher orders of memory can be neglected.

A Gaussian laser beam propagating through collisional plasma heats the electrons non-uniformaly, creating a depressed density duct via ambipolar diffusion. As the beam propagates through the self-made duct its size shrinks due to self-focusing, and marginal rays begin to play a role. This effect is incorporated by expanding the eikonal up to fourth power in r. The radial intensity profile of the laser becomes less steep than Gaussian.

In this paper, exact solutions for the nonlinear Schrödinger (NLS) equation with nonperiodic modulation describing propagation of light in nonlinear media, under three sets of transverse modulation forms of the refractive index are presented. Unlike the reported cases with periodic modulation, the novel ones can accurately describe the behaviour of propagation for a light beam in nonperiodic structures. Moreover, a series of new nonlinear effects of light propagation are displayed. Furthermore, the stability of the solutions is discussed numerically, and the results reveal that these solutions are stable to finite initial perturbations.

The quantum state and plasma screening effects on electron–neutral atom polarization transport collisions are investigated in partially ionized hydrogen plasmas. The screened Buckingham potential model is applied to describe the polarization interaction between the projectile electron and the neutral target atom in partially ionized plasmas. The method of partial waves is applied to represent the electron–atom polarization transport cross-section as a function of the quantum states, Debye length and collision energy. The results show that the plasma screening effects on the polarization transport cross-section are found to be more significant for low collision energies. It is also found that the transport cross-section is significantly increased with increasing quantum states.

A light beam of high photon density and spatially limited cross-section is analysed with respect to its boundary conditions and angular momentum (spin). For Maxwell's equationsin a vacuum state of vanishing electrical field divergence, the exact solutions are found not to be reconcilable with a beam having a limited cross-section and a nonzero spin. Transverse spatial beam derivatives only become possible as an approximation when their characteristic lengths are very large as compared to the relevant wavelengths, but even then there is no spin. A revised electromagnetic theory, based on a nonzero electric field divergence in the vacuum state, leads on the other hand to beam configurations for which there can exist strong transverse derivatives in a boundary region, as well as a nonzero spin. The Poynting vector then has components both in the axial direction of propagation and in the transverse direction along the boundary. The angular momentum, being imagined as an equivalent sum of momenta of the individual photons in the beam interior, is then replaced by a real spin generated and localized in the boundary layer.

The International Symposium on (e,2e), Double Photoionization and Related Topics, and the 13th International Symposium on Polarization and Correlation in Electronic and Atomic Collisions were held concurrently in Buenos Aires, Argentina, from 20 to 28 July 2005. Here, the papers presented at the meetings are reported.

A report is presented of the 13th International Symposium on Electron–Molecule Collisions Physics (Instituto de Fisica, Unicamp, Campinas, Brazil, 27–30 July 2005). This workshop covered low-energy electron interactions with atoms, molecules and condensed matter systems. Several important aspects of this symposium were to bring together theory and experimental advances in this field for gaseous targets as well as showcasing the increasing diversity of electron–molecule collision applications in condensed matter and biological applications. A summary session was held wherein were discussed aspects of the future of the field, including the development of new theoretical and experimental capabilities.