461 research outputs found
Anisotropic symmetrization and Sobolev inequalities on Finsler manifolds with nonnegative Ricci curvature
By using a sharp isoperimetric inequality and an anisotropic symmetrization
argument, we establish Morrey-Sobolev and Hardy-Sobolev inequalities on
-dimensional Finsler manifolds having nonnegative -Ricci curvature; in
some cases we also discuss the sharpness of these functional inequalities. As
applications, by using variational arguments, we guarantee the
existence/multiplicity of solutions for certain eigenvalue problems and
elliptic PDEs involving the Finsler-Laplace operator. Our results are also new
in the Riemannian setting.Comment: 17 page
Mass loss and longevity of gravitationally bound oscillating scalar lumps (oscillatons) in D-dimensions
Spherically symmetric oscillatons (also referred to as oscillating soliton
stars) i.e. gravitationally bound oscillating scalar lumps are considered in
theories containing a massive self-interacting real scalar field coupled to
Einstein's gravity in 1+D dimensional spacetimes. Oscillations are known to
decay by emitting scalar radiation with a characteristic time scale which is,
however, extremely long, it can be comparable even to the lifetime of our
universe. In the limit when the central density (or amplitude) of the
oscillaton tends to zero (small-amplitude limit) a method is introduced to
compute the transcendentally small amplitude of the outgoing waves. The results
are illustrated in detail on the simplest case, a single massive free scalar
field coupled to gravity.Comment: 23 pages, 2 figures, references on oscillons added, version to appear
in Phys. Rev.
Computation of the radiation amplitude of oscillons
The radiation loss of small amplitude oscillons (very long-living, spatially
localized, time dependent solutions) in one dimensional scalar field theories
is computed in the small-amplitude expansion analytically using matched
asymptotic series expansions and Borel summation. The amplitude of the
radiation is beyond all orders in perturbation theory and the method used has
been developed by Segur and Kruskal in Phys. Rev. Lett. 58, 747 (1987). Our
results are in good agreement with those of long time numerical simulations of
oscillons.Comment: 22 pages, 9 figure
Interrelations Between the Neutron's Magnetic Interactions and the Magnetic Aharonov-Bohm Effect
It is proved that the phase shift of a polarized neutron interacting with a
spatially uniform time-dependent magnetic field, demonstrates the same physical
principles as the magnetic Aharonov-Bohm effect. The crucial role of inert
objects is explained, thereby proving the quantum mechanical nature of the
effect. It is also proved that the nonsimply connectedness of the field-free
region is not a profound property of the system and that it cannot be regarded
as a sufficient condition for a nonzero phase shift.Comment: 18 pages, 1 postscript figure, Late
Boson stars and oscillatons in an inflationary universe
Spherically symmetric gravitationally bound, oscillating scalar lumps (boson
stars and oscillatons) are considered in Einstein's gravity coupled to massive
scalar fields in 1+D dimensional de Sitter-type inflationary space-times. We
show that due to inflation bosons stars and oscillatons lose mass through
scalar radiation, but at a rate that is exponentially small when the expansion
rate is slow.Comment: 19 pages, 5 figure
Non exponential relaxation in fully frustrated models
We study the dynamical properties of the fully frustrated Ising model. Due to
the absence of disorder the model, contrary to spin glass, does not exhibit any
Griffiths phase, which has been associated to non-exponential relaxation
dynamics. Nevertheless we find numerically that the model exhibits a stretched
exponential behavior below a temperature T_p corresponding to the percolation
transition of the Kasteleyn-Fortuin clusters. We have also found that the
critical behavior of this clusters for a fully frustrated q-state spin model at
the percolation threshold is strongly affected by frustration. In fact while in
absence of frustration the q=1 limit gives random percolation, in presence of
frustration the critical behavior is in the same universality class of the
ferromagnetic q=1/2-state Potts model.Comment: 7 pages, RevTeX, 11 figs, to appear on Physical Review
Oscillons in dilaton-scalar theories
It is shown by both analytical methods and numerical simulations that
extremely long living spherically symmetric oscillons appear in virtually any
real scalar field theory coupled to a massless dilaton (DS theories). In fact
such "dilatonic" oscillons are already present in the simplest non-trivial DS
theory -- a free massive scalar field coupled to the dilaton. It is shown that
in analogy to the previously considered cases with a single nonlinear scalar
field, in DS theories there are also time periodic quasibreathers (QB)
associated to small amplitude oscillons. Exploiting the QB picture the
radiation law of the small amplitude dilatonic oscillons is determined
analytically.Comment: extended discussion on stability, to appear in JHEP, 29 pages, 7
figure
Theory of the Fano Resonance in the STM Tunneling Density of States due to a Single Kondo Impurity
The conduction electron density of states nearby single magnetic impurities,
as measured recently by scanning tunneling microscopy (STM), is calculated,
taking into account tunneling into conduction electron states only. The Kondo
effect induces a narrow Fano resonance in the conduction electron density of
states, while scattering off the d-level generates a weakly energy dependent
Friedel oscillation. The line shape varies with the distance between STM tip
and impurity, in qualitative agreement with experiments, but is very sensitive
to details of the band structure. For a Co impurity the experimentally observed
width and shift of the Kondo resonance are in accordance with those obtained
from a combination of band structure and strongly correlated calculations.Comment: 4 pages, ReVTeX + 4 figures (Encapsulated Postscript), submitted to
PR
Dissociative recombination of NS+ in collisions with slow electrons
Cross sections and rate coefficients for the Dissociative Recombination (DR)
of the NS+ ion induced by collisions with low-energy electrons are reported for
temperatures between 10 and 1000 K, relevant to a large range of interstellar
cloud temperatures. Uncertainties are discussed for these rates. Comparisons
are made with DR rates for the isovalent NO+ molecular ion which are found to
be much faster. The present findings lead to a moderate dissociative reaction
rate coefficient, smaller by a factor of 2 than the current estimates reported
in the different kinetic databases for a temperature of 10 K. We consider that
our rate coefficients obtained through multichannel quantum defect theory for
NS+ are likely to be better than those displayed in the different kinetic
databases.Comment: 6 pages, 8 figures, 2 table
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