Volume 2, Issue 3

Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities etc.) and they turn into quasiparticles of a new type—defectons, which are characterized not by their position in the crystal lattice but by their quasimomentum and dispersion law. Defecton-defecton and defecton-phonon scattering are considered and an interpolation formula for the diffusion coefficient valid in all interesting temperature and concentration regions is presented. A comparison with the experimental data is made. Some alternative points of view are discussed in detail and the inconsistency of the Kisvarsanyi-Sullivan theory is shown.

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated special functions and the corresponding raising/lowering operators. The equations considered are directly related to some Schrödinger type equations (Pöschl-Teller, Scarf, Morse, etc), and the special functions defined are related to the corresponding bound-state eigenfunctions.

The observational and theoretical status of neutrino oscillations in connection with solar and atmospheric neutrino anomalies is presented briefly. The effect of neutrino oscillations on the evolution of the early Universe is discussed in detail. A short review is given of the standard Big Bang Nucleosynthesis (BBN) and the influence of resonant and non-resonant neutrino oscillations on active neutrinos and on primordial synthesis of He-4. BBN cosmological constraints on neutrino oscillation parameters are discussed.

A Quantum Iterated Function System on a complex projective space is defined through a family of linear operators on a complex Hilbert space. The operators define both the maps and their probabilities by one algebraic formula. Examples with conformal maps (relativistic boosts) on the Bloch sphere are discussed.

Special computer-aided equipment was designed for measurement of biomechanical characteristics of lower part of the spine (L1-L5). When the stress is applied, it is necessary to observe the shift of the sample elements, together with measurement of the spine rigidity. This shift is determined with the help of circular targets fitted to the appropriate vertebra. The targets, illuminated by lamp or laser light, are monitored and their digitalized images are scanned by CCD camera is stored as computer media. The two dimensional Fourier transform of the digital optical signal is obtained by the fast Fourier transform algorithm. The period and direction of the interference fringes determine the size and the direction of the sample shift.

The pion momentum distributions (MDs) in four channels of virtual decay p→B+π, B = N, Δ, N 1/2-(1535), N 1/2+(1440) are calculated in two models, the microscopic model of 3 P 0 scalar q−q fluctuation with the pion as a composite q−q-system and the chiral semi-microscopic model of πq interaction with the pion as a structureless Goldstone boson. The results of the above models are similar for the baryon states B = N, Δ, N 1/2-(1535) but are rather different for the Roper resonance N 1/2+(1440) which corresponds to excitation of two oscillator quanta in the nucleon. The experimental investigation of pion MDs by means of the reaction of quasi-elastic knockout of pion by an electron of a few GeV energy p(e, e′ π)B may be very suitable for Jefferson Laboratory, Virginia (JLab).

We calculate the leptonic constant for the pseudoscalar ground state of the B c meson in the framework of a QCD-motivated potential model taking into account the two-loop anomalous dimension for the heavy quark current in nonrelativistic QCD as matched with full QCD.

A cubic structure of polymer colloid complexes is studied. The technique of the research includes i) an analysis of well-known literature SAXS data; on this basis, ii) constructing a simple model to estimate geometric structure parameters and to obtain a simulated scattering curve; and iii) comparing the model with the real structure obtained from the SAXS data, using the reconstruction of electron density distribution. A bicontinuous structure in cubic mesophases is formed.