On the number of nonequivalent propelinear extended perfect codes

The paper proves that there exist an exponential number of nonequivalent propelinear extended perfect binary codes of length growing to infinity. Specifically, it is proved that all transitive extended perfect binary codes found by Potapov are propelinear. All such codes have small rank, which is one more than the rank of the extended Hamming code of the same length. We investigate the properties of these codes and show that any of them has a normalized propelinear representation

Giant dispersion of critical currents in superconductor with fractal clusters of a normal phase

The influence of fractal clusters of a normal phase on the dynamics of a magnetic flux trapped in a percolative superconductor is considered. The critical current distribution and the current-voltage characteristics of fractal superconducting structures in the resistive state are obtained for an arbitrary fractal dimension of the cluster boundaries. The range of fractal dimensions, where the dispersion of critical currents becomes infinite, is found. It is revealed that the fractality of clusters depresses of the electric field caused by the magnetic flux motion thus increasing the critical current value. It is expected that the maximum current-carrying capability of a superconductor can be achieved in the region of giant dispersion of critical currents.Comment: 7 pages with 3 figure

Tunneling of Bloch electrons through vacuum barrier

Tunneling of Bloch electrons through a vacuum barrier introduces new physical effects in comparison with the textbook case of free (plane wave) electrons. For the latter, the exponential decay rate in the vacuum is minimal for electrons with the parallel component of momentum ${\bf k}_\parallel=0$, and the prefactor is defined by the electron momentum component in the normal to the surface direction. However, the decay rate of Bloch electrons may be minimal at an arbitrary ${\bf k}_\parallel$ (``hot spots''), and the prefactor is determined by the electron's group velocity, rather than by its quasimomentum.Comment: 4 pages, no fig

Interlayer spin-singlet pairing induced by magnetic interactions in an antiferromagnetic superconductor

It is shown that interlayer spin-singlet Cooper pairing is induced by magnetic interactions in a metallic antiferromagnet of stacked conductive layers in which each layer is ferromagnetically polarized and they order antiferromagnetically in stacking direction. As a result, the antiferromagnetic long-range order and superconductivity coexist at low temperatures. It is shown that T_AF > T_c except for in a very limited parameter region unless T_AF = 0, where T_AF and T_c denote the antiferromagnetic and superconducting transition temperatures, respectively. It is found that the exchange field caused by the spontaneous staggered magnetization does not affect superconductivity at all, even if it is very large. The resultant superconducting order parameter has a horizontal line node, and is isotropic in spin space in spite of the anisotropy of the background magnetic order. We discuss the possible relevance of the present mechanism to the antiferromagnetic heavy fermion superconductors UPd_2Al_3 and CePt_3Si.Comment: 5 pages, 3 figures, in revtex

Single pion electro-- and neutrinoproduction on heavy targets

We present a calculation of single pion electroproduction cross sections on heavy targets in the kinematic region of the Delta(1232) resonance. Final state interactions of the pions are taken into account using the pion multiple scattering model of Adler, Nussinov and Paschos (ANP model). For electroproduction and neutral current reactions we obtain results for carbon, oxygen, argon and iron targets and find a significant reduction of the W-spectra for pi^0 as compared to the free nucleon case. On the other hand, the charged pion spectra are only little affected by final state interactions. Measurements of such cross sections with the CLAS detector at JLAB could help to improve our understanding of pion rescattering effects and serve as important/valuable input for calculations of single pion neutrinoproduction on heavy targets relevant for current and future long baseline neutrino experiments. Two ratios, in Eq. (3.8) and (3.10), will test important properties of the model.Comment: 21 pages, 8 figure