Table of contents

We review different calculation methods of the one-link integral, appearing in the strong coupling approximation in the lattice QCD. Some new formulae useful in the case of lattice QCD with Susskind fermions are also presented.

The stationary heat conduction problem with a periodic conductivity matrix is studied. An averaged variational principle based on the ideas of Whitham [1] is formulated, that gives results which coincide with those predicted by the homogenization procedure [2].

The correspondence between the results given by different variants of the Method of Continued Fractions is shown. Approximate solutions of the Lippmann-Schwinger equation obtained with help of the MCF can be expressed in terms of Padé approximants. Explicit formulas for the coefficients of the continued fractions in terms of the coefficients of the Born expansion are given. The way of constructing the continued fraction in a degenerate case, i.e., when some Hankel determinants vanish, is also discussed.

Let du_i/dt = F_i(u) (i = 1,..., n) be a scale invariant autonomous system of first order differential equations, where the F_i's are polynomials. The following questions will be discussed: (i) Does the scale invariance determine the dominant behaviour of the Painlevé analysis? (ii) Assume that du_i/dt = F_i(u) admits a Lax representation. Does the Lax representation provide all the first integrals of the dynamical system? (iii) Let I₁,..., I_n-1 be first integrals of du_i/dt = F_i(u). Is the dynamical system constructed from the first integrals I₁,..., I_n-1 within the Nambu mechanics given by du_i/dt = F_i(u)?

Two ¹Σ⁺-¹Σ⁺ systems of the isotopic molecules ¹²⁰Sn¹⁶O and ¹²⁰Sn¹⁸O in the wavelength region 1720-1780 Å have been rotationally analyzed. Molecular constants for the upper states are given. Further out to shorter wavelengths three additional band systems have been observed but not rotationally analyzed.

A spectral light source utilising a supersonic jet and a hollow cathode discharge is described. It is shown that both the rotational temperature, measured on the N₂⁺B-X(0, 0) band, and the translational temperature measured on the 5015 He line are about 15 K in the cold component of the jet. The translational temperature was measured with the MEGA-spectrometer set to a spectral resolution of 0.9 × 10⁶. The discharge is realised in a very simple construction offering a new tool for sub-Doppler spectroscopy.

Informatoin entropy has been employed in the density-functional theory to derive some useful relations between atomic expectation values, and these relations are numerically tested by Hartree-Fock atomic expectation values.

Radiative transition rates, autoionization rates, and transition energies are calculated for 3l3l' autoionizing states of helium-like argon and silicon. The effects of configuration mixing and spin-orbit interaction between states of the same parity are taken into account. The branching ratio associated with each open channel is listed. The most dominant deexcitation channels are found to be the processes that lead to the removal of one of the electrons to the continuum and the other to the 2p subshell. This confirms quantitatively the prediction of Fano and Cooper that the autoionization channels requiring the least energy are most likely.

Experimental data for the spin-orbital interaction and Λ-doubling parameters of the OH radical in the ground electronic state X²Π_i are analysed in order to extract the radial dependence of the corresponding functions. The procedure is compared with those employed in previous work.

The production, storage, and investigation of atomic antimatter is considered. The formation of antihydrogen as well as that of more complex systems such as ⁺, ₂⁻, and are discussed. The main arguments for the production and investigation of these systems are given. Different production scenarios and problems to be solved are examined. Potential experiments are described, in particular those using polarized antiprotons obtained from antihydrogen.

A relativistic version of the variational perturbation method is extended to apply to excited states of the Dirac equation. It is proved that the value of the Hylleraas functional is an upper bound to the exact second-order (proportional to c⁻⁴) correction to the energy. In order to demonstrate the usefulness of this approach to the problem of optimising non-linear parameters the method is applied to the special case of hydrogen-like atoms. The first-order relativistic corrections to the wavefunctions for some s, p and d states have been approximated in terms of expontential functions.

Experimental lifetimes of several levels in the 2p⁵ 3p and 3d configurations in Ne-like sulphur, S VII, and argon, Ar IX, have been determined by the beam-foil technique. The ANDC method for cascade correction has been applied in the analyses of the 3p decay curves. The results are generally in good agreement with recent theoretical values except for the 3p³D levels for which significant deviations are observed. Similar discrepancies have also been observed in the isoelectronic Cl VIII system.

The distribution of trapped particles in a solitary BGK wave is found by modeling the potential shape. This distribution is used in the stability analysis of a small amplitude solitary wave. It is shown that such a wave is stable for perturbation wavelengths much smaller than its width. The Lewis-Symon method is used for the normal mode perturbations localized in the BGK wave region. In this case an instability similar to the fluid beam-type instability in a homogeneous plasma takes place.

A representation of a finite Larmor radius plasma is proposed, which permits the transition r_L → ∞ without becoming mathematically ill-posed. It is being used in a two-dimensional guiding center plasma spectral code and may have useful analytical applications. The ions are represented as guiding centers and the Larmor radius is averaged analytically for every Fourier-mode. Finite Larmor radius densities and velocities are thus obtained from guiding center quantities by application of a filter in wave vector space.

Analytic expressions for the density of neutral hydrogen atoms in a hydrogen half-space plasma with reflecting boundary and internal (line and point) sources are derived and discussed. A finite-slab solution is additionally reported for the case of a non-reflecting wall.

Satellite (IC-B-1300) data on the electromagnetic structures in the high-latitude ionosphere are presented. One can observe three kinds of vortices, namely vortex chains as well as solitary dipolar and monopolar vortex structures. The theoretical treatment that is carried out in the present paper is in reasonable agreement with the observations.

We present solutions of the wave equations which show that oscillatory structures will develop when a powerful radio wave beam propagates through the defocusing region of the ionosphere.

The name and the implications of the Boussinesq approximation for gravity waves in an incompressible, infinitely stratified atmosphere at rest are discussed together with the conditions for its validity. The most important conclusion is that for this approximation to be valid, the relative amplitude of the wave, with respect to the equilibrium value, has to be much smaller than the quotient of the wavelength in the direction of the density gradient and the length of that gradient. In its turn this product has to be much smaller than one.

An iterative technique of finding a solution of the ideal MHD equilibrium equations for a three-dimensional net-free-current stellarator with anisotropic pressure in a magnetic coordinate representation is described. In every iteration step the plasma current is determined and the associated magnetic field is calculated. This iterative technique describes a fixed boundary equilibrium.

Reaction-diffusion equations are used to describe dynamic evolution of densities or populations for certain forms of initial conditions in space. New results from extensive investigations on such equations are reported. These allow for arbitrary powers of the dependence on density for the diffusion and reaction processes. Primarily, creative reactions are considered but, for comparison, some cases of annihilation reactions are also described. Convenient methods of nonlinear analysis are developed for the purpose of describing in particular the evolution in time of characteristic widths and amplitudes of profiles. The theory is presented in a unified form including one, two and three space dimensions. A rich variety of possible solutions are obtained, including, beside some exact localized solutions, also "collapse" and "anti-collapse" solutions as well as other generalized forms of solutions. The analytical results are supported by computer experiments.

We propose a model for superconductivity in the 123 materials which attributes a central role to the twin boundaries. These boundaries, parallel to the {110} planes, are always observed in the superconducting phases. The model assumes that the twin boundaries support interfacial states at the Fermi level. The electrons trapped in these states condense into Cooper pairs due to attraction mediated predominantly by electron-hole transitions (excitons) between the Cu-O planes and the Cu-O chain bands. A representative two band model yields an analytic estimate of the order of the experimental value. Some implications of the model are briefly discussed.

The density of states of a hydrogen atom on a linear chain is calculated using the Anderson-Newns Hamiltonian with a many-electron basis set. The total cross-section of EELS is considered as a superposition of five different excitations represented by operators, taking into account both adsorbate and substrate levels; the dynamic form factors of the five excitations are calculated and their main features discussed, for different occupations and widths of the band. The Hamiltonian is supplemented with a Coulomb interaction U_mm between the substrate electrons and another, U_am, between a substrate electron and an adsorbate electron/hole, their effects in the results being discussed.

The details of the magnetic phase diagram of Fe_1-xAl_x alloys are discussed within a model exactly, describing the effects of short range chemical order and clustering. A good fitting to experimental data is obtained assuming that in the range of low concentrations of Al the clustering dominates while for other concentrations the partial short range chemical ordering exists. It is also explained why the temperature range of the re-entrant spin glass phenomenon is so narrow.