26 research outputs found
On the Coulomb-Sturmian matrix elements of the Coulomb Green's operator
The two-body Coulomb Hamiltonian, when calculated in Coulomb-Sturmian basis,
has an infinite symmetric tridiagonal form, also known as Jacobi matrix form.
This Jacobi matrix structure involves a continued fraction representation for
the inverse of the Green's matrix. The continued fraction can be transformed to
a ratio of two hypergeometric functions. From this result we find
an exact analytic formula for the matrix elements of the Green's operator of
the Coulomb Hamiltonian.Comment: 8 page
Accumulation of three-body resonances above two-body thresholds
We calculate resonances in three-body systems with attractive Coulomb
potentials by solving the homogeneous Faddeev-Merkuriev integral equations for
complex energies. The equations are solved by using the Coulomb-Sturmian
separable expansion approach. This approach provides an exact treatment of the
threshold behavior of the three-body Coulombic systems. We considered the
negative positronium ion and, besides locating all the previously know -wave
resonances, we found a whole bunch of new resonances accumulated just slightly
above the two-body thresholds. The way they accumulate indicates that probably
there are infinitely many resonances just above the two-body thresholds, and
this might be a general property of three-body systems with attractive Coulomb
potentials.Comment: 4 pages, 3 figure
Resonant-state solution of the Faddeev-Merkuriev integral equations for three-body systems with Coulomb potentials
A novel method for calculating resonances in three-body Coulombic systems is
proposed. The Faddeev-Merkuriev integral equations are solved by applying the
Coulomb-Sturmian separable expansion method. The S-state
resonances up to threshold are calculated.Comment: 6 pages, 2 ps figure
Self-dual solitons in N=2 supersymmetric semilocal Chern-Simons theory
We embed the semilocal Chern-Simons-Higgs theory into an N=2 supersymmetric
system. We construct the corresponding conserved supercharges and derive the
Bogomol'nyi equations of the model from supersymmetry considerations. We show
that these equations hold provided certain conditions on the coupling constants
as well as on the Higgs potential of the system, which are a consequence of the
huge symmetry of the theory, are satisfied. They admit string-like solutions
which break one half of the supersymmetries --BPS Chern-Simons semilocal cosmic
strings-- whose magnetic flux is concentrated at the center of the vortex. We
study such solutions and show that their stability is provided by supersymmetry
through the existence of a lower bound for the energy, even though the manifold
of the Higgs vacuum does not contain non-contractible loops.Comment: 12 pages, LaTeX, no figures, to appear in Modern Physics Letters
Phases of dual superconductivity and confinement in softly broken N=2 supersymmetric Yang-Mills theories
We study the electric flux tubes that undertake color confinement in N=2
supersymmetric Yang-Mills theories softly broken down to N=1 by perturbing with
the first two Casimir operators. The relevant Abelian Higgs model is not the
standard one due to the presence of an off-diagonal coupling among different
magnetic U(1) factors. We perform a preliminary study of this model at a
qualitative level. BPS vortices are explicitely obtained for particular values
of the soft breaking parameters. Generically however, even in the ultrastrong
scaling limit, vortices are not critical but live in a "hybrid" type II phase.
Also, ratios among string tensions are seen to follow no simple pattern. We
examine the situation at the half Higgsed vacua and find evidence for solutions
with the behaviour of superconducting strings. In some cases they are solutions
to BPS equations.Comment: 15 pages, 1 figure, revtex; v2: typos corrected, final versio
Three-potential formalism for the three-body scattering problem with attractive Coulomb interactions
A three-body scattering process in the presence of Coulomb interaction can be
decomposed formally into a two-body single channel, a two-body multichannel and
a genuine three-body scattering. The corresponding integral equations are
coupled Lippmann-Schwinger and Faddeev-Merkuriev integral equations. We solve
them by applying the Coulomb-Sturmian separable expansion method. We present
elastic scattering and reaction cross sections of the system both below
and above the threshold. We found excellent agreements with previous
calculations in most cases.Comment: 12 pages, 3 figure
Supersymmetric Electroweak Cosmic Strings
We study the connection between supersymmetry and a topological bound
in a two-Higgs-doublet system with an gauge group. We derive the Bogomol'nyi equations from
supersymmetry considerations showing that they hold provided certain conditions
on the coupling constants, which are a consequence of the huge symmetry of the
theory, are satisfied. Their solutions, which can be interpreted as electroweak
cosmic strings breaking one half of the supersymmetries of the theory, are
studied. Certain interesting limiting cases of our model which have recently
been considered in the literature are finally analyzed.Comment: 20 pages, RevTe
Bogomol'nyi Equations of Maxwell-Chern-Simons vortices from a generalized Abelian Higgs Model
We consider a generalization of the abelian Higgs model with a Chern-Simons
term by modifying two terms of the usual Lagrangian. We multiply a dielectric
function with the Maxwell kinetic energy term and incorporate nonminimal
interaction by considering generalized covariant derivative. We show that for a
particular choice of the dielectric function this model admits both topological
as well as nontopological charged vortices satisfying Bogomol'nyi bound for
which the magnetic flux, charge and angular momentum are not quantized. However
the energy for the topolgical vortices is quantized and in each sector these
topological vortex solutions are infinitely degenerate. In the nonrelativistic
limit, this model admits static self-dual soliton solutions with nonzero finite
energy configuration. For the whole class of dielectric function for which the
nontopological vortices exists in the relativistic theory, the charge density
satisfies the same Liouville equation in the nonrelativistic limit.Comment: 30 pages(4 figures not included), RevTeX, IP/BBSR/93-6
d-Wave Superconductivity Induced by Chern-Simons Term in High- Cuprates
We show that a Chern-Simons term for a gauge field describing a fluctuation
of spins is induced by integrating out hole fields in the presence of
spin-orbit coupling which originates from a buckling of the CuO plane.
Through the Chern-Simons term, holes behave like skyrmion excitations in a spin
system and become a superconducting state with symmetry after the
antiferromagnetic long-range order is destroyed.Comment: 4 pages, 1 figure, the condition of taking continuum limit included,
references added, typos corrected, to be published in Journal of Physical
Society of Japa