48 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
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
Extended Superconformal Galilean Symmetry in Chern-Simons Matter Systems
We study the nonrelativistic limit of the supersymmetric Chern-Simons
matter system. We show that in addition to Galilean invariance the model admits
a set of symmetries generated by fermionic charges, which can be interpreted as
an {\it extended Galilean supersymmetry }. The system also possesses a hidden
conformal invariance and then the full group of symmetries is the {\it extended
superconformal Galilean} group. We also show that imposing extended
superconformal Galilean symmetry determines the values of the coupling
constants in such a way that their values in the bosonic sector agree with the
values of Jackiw and Pi for which self-dual equation exist. We finally analyze
the second quantized version of the model and the two-particle sector.Comment: 32 double-spaced page
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
Static solitons with non-zero Hopf number
We investigate a generalized non-linear O(3) -model in three space
dimensions where the fields are maps . Such maps are
classified by a homotopy invariant called the Hopf number which takes integer
values. The model exhibits soliton solutions of closed vortex type which have a
lower topological bound on their energies. We explicitly compute the fields for
topological charge 1 and 2 and discuss their shapes and binding energies. The
effect of an additional potential term is considered and an approximation is
given for the spectrum of slowly rotating solitons.Comment: 13 pages, RevTeX, 7 Postscript figures, minor changes have been made,
a reference has been corrected and a figure replace
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
Prospects for precision measurements of atomic helium using direct frequency comb spectroscopy
We analyze several possibilities for precisely measuring electronic
transitions in atomic helium by the direct use of phase-stabilized femtosecond
frequency combs. Because the comb is self-calibrating and can be shifted into
the ultraviolet spectral region via harmonic generation, it offers the prospect
of greatly improved accuracy for UV and far-UV transitions. To take advantage
of this accuracy an ultracold helium sample is needed. For measurements of the
triplet spectrum a magneto-optical trap (MOT) can be used to cool and trap
metastable 2^3S state atoms. We analyze schemes for measuring the two-photon
interval, and for resonant two-photon excitation to high
Rydberg states, . We also analyze experiments on the
singlet-state spectrum. To accomplish this we propose schemes for producing and
trapping ultracold helium in the 1^1S or 2^1S state via intercombination
transitions. A particularly intriguing scenario is the possibility of measuring
the transition with extremely high accuracy by use of
two-photon excitation in a magic wavelength trap that operates identically for
both states. We predict a ``triple magic wavelength'' at 412 nm that could
facilitate numerous experiments on trapped helium atoms, because here the
polarizabilities of the 1^1S, 2^1S and 2^3S states are all similar, small, and
positive.Comment: Shortened slightly and reformatted for Eur. Phys. J.
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