1,610 research outputs found
Soliton Lattice and Single Soliton Solutions of the Associated Lam\'e and Lam\'e Potentials
We obtain the exact nontopological soliton lattice solutions of the
Associated Lam\'e equation in different parameter regimes and compute the
corresponding energy for each of these solutions. We show that in specific
limits these solutions give rise to nontopological (pulse-like) single
solitons, as well as to different types of topological (kink-like) single
soliton solutions of the Associated Lam\'e equation. Following Manton, we also
compute, as an illustration, the asymptotic interaction energy between these
soliton solutions in one particular case. Finally, in specific limits, we
deduce the soliton lattices, as well as the topological single soliton
solutions of the Lam\'e equation, and also the sine-Gordon soliton solution.Comment: 23 pages, 5 figures. Submitted to J. Math. Phy
Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition
We show that a type of linear superposition principle works for several
nonlinear differential equations. Using this approach, we find periodic
solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear
Schrodinger (NLS) equation, the model, the sine-Gordon
equation and the Boussinesq equation by making appropriate linear
superpositions of known periodic solutions. This unusual procedure for
generating solutions is successful as a consequence of some powerful, recently
discovered, cyclic identities satisfied by the Jacobi elliptic functions.Comment: 19 pages, 4 figure
Angular separations of the lensed QSO images
We have analyzed the observed image separations of the gravitationally lensed
images of QSOs for a possible correlation with the source redshift. Contrary to
the previously noted anti-correlation based on a smaller data set, no
correlation is found for the currently available data. We have calculated the
average image separations of the lensed QSOs as a function of source redshifts,
for isothermal spheres with cores in a flat universe, taking into account the
amplification bias caused by lensing. The shape of the distribution of average
image separation as a function of redshift is very robust and is insensitive to
most model parameters. Observations are found to be roughly consistent with the
theoretical results for models which assume the lens distribution to be (i)
Schechter luminosity function which, however, can not produce images with large
separation and (ii) the mass condensations in a cold dark matter universe, as
given by the Press-Schechter theory if an upper limit of 1-7
M is assumed on the mass of the condensations.Comment: 20 pages, 7 postscript figures, accepted for publication in The
Astrophysical Journa
Island diffusion on metal fcc(100) surfaces
We present Monte Carlo simulations for the size and temperature dependence of
the diffusion coefficient of adatom islands on the Cu(100) surface. We show
that the scaling exponent for the size dependence is not a constant but a
decreasing function of the island size and approaches unity for very large
islands. This is due to a crossover from periphery dominated mass transport to
a regime where vacancies diffuse inside the island. The effective scaling
exponents are in good agreement with theory and experiments.Comment: 13 pages, 2 figures, to be published in Phys. Rev. Let
Barrier Penetration for Supersymmetric Shape-Invariant Potentials
Exact reflection and transmission coefficients for supersymmetric
shape-invariant potentials barriers are calculated by an analytical
continuation of the asymptotic wave functions obtained via the introduction of
new generalized ladder operators. The general form of the wave function is
obtained by the use of the F-matrix formalism of Froman and Froman which is
related to the evolution of asymptotic wave function coefficients
Hall effects in Bose-Einstein condensates in a rotating optical lattice
Using the Kubo formalism, we demonstrate fractional quantum Hall features in
a rotating Bose-Einstein condensate in a co-rotating two-dimensional optical
lattice. The co-rotating lattice and trap potential allow for an effective
magnetic field and compensation of the centrifugal potential. Fractional
quantum Hall features are seen for the single-particle system and for few
strongly interacting many-particle systems.Comment: 11 pages, 13 figure
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
Testing Hall-Post Inequalities With Exactly Solvable N-Body Problems
The Hall--Post inequalities provide lower bounds on -body energies in
terms of -body energies with . They are rewritten and generalized to
be tested with exactly-solvable models of Calogero-Sutherland type in one and
higher dimensions. The bound for spinless fermions in one dimension is
better saturated at large coupling than for noninteracting fermions in an
oscillatorComment: 7 pages, Latex2e, 2 .eps figure
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