30,422 research outputs found
Relativistic Effects of Mixed Vector-Scalar-Pseudoscalar Potentials for Fermions in 1+1 Dimensions
The problem of fermions in the presence of a pseudoscalar plus a mixing of
vector and scalar potentials which have equal or opposite signs is
investigated. We explore all the possible signs of the potentials and discuss
their bound-state solutions for fermions and antifermions. The cases of mixed
vector and scalar P\"{o}schl-Teller-like and pseudoscalar kink-like potentials,
already analyzed in previous works, are obtained as particular cases
Unified Treatment of Mixed Vector-Scalar Screened Coulomb Potentials for Fermions
The problem of a fermion subject to a general mixing of vector and scalar
screened Coulomb potentials in a two-dimensional world is analyzed and
quantization conditions are found.Comment: 7 page
On Duffin-Kemmer-Petiau particles with a mixed minimal-nonminimal vector coupling and the nondegenerate bound states for the one-dimensional inversely linear background
The problem of spin-0 and spin-1 bosons in the background of a general mixing
of minimal and nonminimal vector inversely linear potentials is explored in a
unified way in the context of the Duffin-Kemmer-Petiau theory. It is shown that
spin-0 and spin-1 bosons behave effectively in the same way. An orthogonality
criterion is set up and it is used to determine uniquely the set of solutions
as well as to show that even-parity solutions do not exist.Comment: 10 page
Stationary states of fermions in a sign potential with a mixed vector-scalar coupling
The scattering of a fermion in the background of a sign potential is
considered with a general mixing of vector and scalar Lorentz structures with
the scalar coupling stronger than or equal to the vector coupling under the
Sturm-Liouville perspective. When the vector coupling and the scalar coupling
have different magnitudes, an isolated solution shows that the fermion under a
strong potential can be trapped in a highly localized region without
manifestation of Klein's paradox. It is also shown that the lonely bound-state
solution disappears asymptotically as one approaches the conditions for the
realization of spin and pseudospin symmetries.Comment: 4 figure
Scattering and bound states of fermions in a mixed vector-scalar smooth step potential
The scattering of a fermion in the background of a smooth step potential is
considered with a general mixing of vector and scalar Lorentz structures with
the scalar coupling stronger than or equal to the vector coupling.
Charge-conjugation and chiral-conjugation transformations are discussed and it
is shown that a finite set of intrinsically relativistic bound-state solutions
appears as poles of the transmission amplitude. It is also shown that those
bound solutions disappear asymptotically as one approaches the conditions for
the realization of the so-called spin and pseudospin symmetries in a
four-dimensional space-time.Comment: 5 figures. arXiv admin note: substantial text overlap with
arXiv:1310.847
Relativistic Coulomb scattering of spinless bosons
The relativistic scattering of spin-0 bosons by spherically symmetric Coulomb
fields is analyzed in detail with an arbitrary mixing of vector and scalar
couplings. It is shown that the partial wave series reduces the scattering
amplitude to the closed Rutherford formula exactly when the vector and scalar
potentials have the same magnitude, and as an approximation for weak fields.
The behavior of the scattering amplitude near the conditions that furnish its
closed form is also discussed. Strong suppressions of the scattering amplitude
when the vector and scalar potentials have the same magnitude are observed
either for particles or antiparticles with low incident momentum. We point out
that such strong suppressions might be relevant in the analysis of the
scattering of fermions near the conditions for the spin and pseudospin
symmetries. From the complex poles of the partial scattering amplitude the
exact closed form of bound-state solutions for both particles and antiparticles
with different scenarios for the coupling constants are obtained. Perturbative
breaking of the accidental degeneracy appearing in a pair of special cases is
related to the nonconservation of the Runge-Lenz vector
Spin and pseudospin symmetries of the Dirac equation with confining central potentials
We derive the node structure of the radial functions which are solutions of
the Dirac equation with scalar and vector confining central potentials,
in the conditions of exact spin or pseudospin symmetry, i.e., when one has
, where is a constant. We show that the node structure for exact
spin symmetry is the same as the one for central potentials which go to zero at
infinity but for exact pseudospin symmetry the structure is reversed. We obtain
the important result that it is possible to have positive energy bound
solutions in exact pseudospin symmetry conditions for confining potentials of
any shape, including naturally those used in hadron physics, from nuclear to
quark models. Since this does not happen for potentials going to zero at large
distances, used in nuclear relativistic mean-field potentials or in the atomic
nucleus, this shows the decisive importance of the asymptotic behavior of the
scalar and vector central potentials on the onset of pseudospin symmetry and on
the node structure of the radial functions. Finally, we show that these results
are still valid for negative energy bound solutions for anti-fermions.Comment: 7 pages, uses revtex macro
A Rice method proof of the Null-Space Property over the Grassmannian
The Null-Space Property (NSP) is a necessary and sufficient condition for the
recovery of the largest coefficients of solutions to an under-determined system
of linear equations. Interestingly, this property governs also the success and
the failure of recent developments in high-dimensional statistics, signal
processing, error-correcting codes and the theory of polytopes. Although this
property is the keystone of -minimization techniques, it is an open
problem to derive a closed form for the phase transition on NSP. In this
article, we provide the first proof of NSP using random processes theory and
the Rice method. As a matter of fact, our analysis gives non-asymptotic bounds
for NSP with respect to unitarily invariant distributions. Furthermore, we
derive a simple sufficient condition for NSP.Comment: 18 Pages, some Figure
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