Scattering on two Aharonov-Bohm vortices with opposite fluxes

The scattering of an incident plane wave on two Aharonov-Bohm vortices with opposite fluxes is considered in detail. The presence of the vortices imposes non-trivial boundary conditions for the partial waves on a cut joining the two vortices. These conditions result in an infinite system of equations for scattering amplitudes between incoming and outgoing partial waves, which can be solved numerically. The main focus of the paper is the analytic determination of the scattering amplitude in two limits, the small flux limit and the limit of small vortex separation. In the latter limit the dominant contribution comes from the S-wave amplitude. Calculating it, however, still requires solving an infinite system of equations, which is achieved by the Riemann-Hilbert method. The results agree well with the numerical calculations

The Cauchy Operator for Basic Hypergeometric Series

We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's ${}_2\phi_1$ transformation formula and Sears' ${}_3\phi_2$ transformation formula can be easily obtained by the symmetric property of some parameters in operator identities. The Cauchy operator involves two parameters, and it can be considered as a generalization of the operator $T(bD_q)$. Using this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy integral, Sears' two-term summation formula, as well as the $q$-analogues of Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for the study of the bivariate Rogers-Szeg\"o polynomials, or the continuous big $q$-Hermite polynomials.Comment: 21 pages, to appear in Advances in Applied Mathematic

Peculiar Behavior of Si Cluster Ions in Solid Al

A peculiar ion behavior is found in a Si cluster, moving with a speed of ~0.22c (c: speed of light) in a solid Al plasma: the Si ion, moving behind the forward moving Si ion closely in a several angstrom distance in the cluster, feels the wake field generated by the forward Si. The interaction potential on the rear Si may balance the deceleration backward force by itself with the acceleration forward force by the forward Si in the longitudinal moving direction. The forward Si would be decelerated normally. However, the deceleration of the rear Si, moving behind closely, would be reduced significantly, and the rear Si may catch up and overtake the forward moving Si in the cluster during the Si cluster interaction with the high-density Al plasma

Finite Form of the Quintuple Product Identity

The celebrated quintuple product identity follows surprisingly from an almost-trivial algebraic identity, which is the limiting case of the terminating q-Dixon formula.Comment: 1 pag

Multiband effects on the conductivity for a multiband Hubbard model

The newly discovered iron-based superconductors have attracted lots of interests, and the corresponding theoretical studies suggest that the system should have six bands. In this paper, we study the multiband effects on the conductivity based on the exact solutions of one-dimensional two-band Hubbard model. We find that the orbital degree of freedom might enhance the critical value $U_c$ of on-site interaction of the transition from a metal to an insulator. This observation is helpful to understand why undoped High-$T_c$ superconductors are usually insulators, while recently discovered iron-based superconductors are metal. Our results imply that the orbital degree of freedom in the latter cases might play an essential role.Comment: 4 pages, 5 figure

Neutrino masses, leptogenesis and dark matter in hybrid seesaw

We suggest a hybrid seesaw model where relatively ``light''right-handed neutrinos give no contribution to the neutrino mass matrix due to a special symmetry. This allows their Yukawa couplings to the standard model particles to be relatively strong, so that the standard model Higgs boson can decay dominantly to a left and a right-handed neutrino, leaving another stable right-handed neutrino as cold dark matter. In our model neutrino masses arise via the type-II seesaw mechanism, the Higgs triplet scalars being also responsible for the generation of the matter-antimatter asymmetry via the leptogenesis mechanism.Comment: 4 page