28,697 research outputs found
The Dirichlet Problem for Curvature Equations in Riemannian Manifolds
We prove the existence of classical solutions to the Dirichlet problem for a
class of fully nonlinear elliptic equations of curvature type on Riemannian
manifolds. We also derive new second derivative boundary estimates which allows
us to extend some of the existence theorems of Caffarelli, Nirenberg and Spruck
[4] and Ivochkina, Trundinger and Lin [19] to more general curvature functions
and less convex domains.Comment: 32 pages, no figures. Final version. Paper accepted to publication in
Indiana University Mathematics Journa
Gravity localization on hybrid branes
This work deals with gravity localization on codimension-1 brane worlds
engendered by compacton-like kinks, the so-called hybrid branes. In such
scenarios, the thin brane behaviour is manifested when the extra dimension is
outside the compact domain, where the energy density is non-trivial, instead of
asymptotically as in the usual thick brane models. The zero mode is trapped in
the brane, as required. The massive modes, although are not localized in the
brane, have important phenomenological implications such as corrections to the
Newton's law. We study such corrections in the usual thick domain wall and in
the hybrid brane scenarios. By means of suitable numerical methods, we attain
the mass spectrum for the graviton and the corresponding wavefunctions. The
spectra possess the usual linearly increasing behaviour from the Kaluza-Klein
theories. Further, we show that the 4D gravitational force is slightly
increased at short distances. The first eigenstate contributes highly for the
correction to the Newton's law. The subsequent normalized solutions have
diminishing contributions. Moreover, we find out that the phenomenology of the
hybrid brane is not different from the usual thick domain wall. The use of
numerical techniques for solving the equations of the massive modes is useful
for matching possible phenomenological measurements in the gravitational law as
a probe to warped extra dimensions.Comment: 15 pages, 11 figure
Stern-Gerlach Entanglement in Spinor Bose-Einstein Condensates
Entanglement of spin and position variables produced by spatially
inhomogeneous magnetic fields of Stern-Gerlach type acting on spinor
Bose-Einstein condensates may lead to interference effects at the level of
one-boson densities. A model is worked out for these effects which is amenable
to analytical calculation for gaussian shaped condensates. The resulting
interference effects are sensitive to the spin polarization properties of the
condensate.Comment: 9 pages, 2 figure
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