39 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
Faddeev-Merkuriev equations for resonances in three-body Coulombic systems
We reconsider the homogeneous Faddeev-Merkuriev integral equations for
three-body Coulombic systems with attractive Coulomb interactions and point out
that the resonant solutions are contaminated with spurious resonances. The
spurious solutions are related to the splitting of the attractive Coulomb
potential into short- and long-range parts, which is inherent in the approach,
but arbitrary to some extent. By varying the parameters of the splitting the
spurious solutions can easily be ruled out. We solve the integral equations by
using the Coulomb-Sturmian separable expansion approach. This solution method
provides an exact description of the threshold phenomena. We have found several
new S-wave resonances in the e- e+ e- system in the vicinity of thresholds.Comment: LaTeX with elsart.sty 13 pages, 5 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
Quantum corrections to the mass of the supersymmetric vortex
We calculate quantum corrections to the mass of the vortex in N=2
supersymmetric abelian Higgs model in (2+1) dimensions. We put the system in a
box and apply the zeta function regularization. The boundary conditions
inevitably violate a part of the supersymmetries. Remaining supersymmetry is
however enough to ensure isospectrality of relevant operators in bosonic and
fermionic sectors. A non-zero correction to the mass of the vortex comes from
finite renormalization of couplings.Comment: Latex, 18 pp; v2 reference added; v3 minor change
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
Quantum Hall Ferromagnets: Induced Topological term and electromagnetic interactions
The quantum Hall ground state in materials like GaAs is well known
to be ferromagnetic in nature. The exchange part of the Coulomb interaction
provides the necessary attractive force to align the electron spins
spontaneously. The gapless Goldstone modes are the angular deviations of the
magnetisation vector from its fixed ground state orientation. Furthermore, the
system is known to support electrically charged spin skyrmion configurations.
It has been claimed in the literature that these skyrmions are fermionic owing
to an induced topological Hopf term in the effective action governing the
Goldstone modes. However, objections have been raised against the method by
which this term has been obtained from the microscopics of the system. In this
article, we use the technique of the derivative expansion to derive, in an
unambiguous manner, the effective action of the angular degrees of freedom,
including the Hopf term. Furthermore, we have coupled perturbative
electromagnetic fields to the microscopic fermionic system in order to study
their effect on the spin excitations. We have obtained an elegant expression
for the electromagnetic coupling of the angular variables describing these spin
excitations.Comment: 23 pages, Plain TeX, no figure