33,910 research outputs found
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 transformation formula and Sears'
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 . Using
this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy
integral, Sears' two-term summation formula, as well as the -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
-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
Tidal Waves -- a non-adiabatic microscopic description of the yrast states in near-spherical nuclei
The yrast states of nuclei that are spherical or weakly deformed in their
ground states are described as quadrupole waves running over the nuclear
surface, which we call "tidal waves". The energies and E2 transition
probabilities of the yrast states in nuclides with = 44, 46, 48 and are calculated by means of the cranking model in a microscopic
way. The nonlinear response of the nucleonic orbitals results in a strong
coupling between shape and single particle degrees of freedom
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 of on-site interaction of the transition from a metal to an
insulator. This observation is helpful to understand why undoped High-
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
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