4,180 research outputs found
Determination of matrix potential from scattering matrix
(i) For the matrix Schr\"{o}dinger operator on the half line, it is shown
that if the potential exponentially decreases fast enough then only the
scattering matrix uniquely determines the self-adjoint potential and the
boundary condition. (ii) For the matrix Schr\"{o}dinger operator on the full
line, it is shown that if the potential exponentially decreases fast enough
then the scattering matrix (or equivalently, the transmission coefficient and
reflection coefficient) uniquely determine the potential. If the potential
vanishes on then only the left reflection coefficient uniquely
determine the potential.Comment: 9 page
Inverse spectral problems for the Sturm-Liouville operator with discontinuity
In this work, we consider the Sturm-Liouville operator on a finite interval
with discontinuous conditions at . We prove that if the potential
is known a priori on a subinterval with , then parts of two
spectra can uniquely determine the potential and all parameters in
discontinuous conditions and boundary conditions. For the case , parts
of either one or two spectra can uniquely determine the potential and a part of
parameters.Comment: 13 page
Solvability of the inverse scattering problem for the selfadjoint matrix Schrodinger operator on the half line
In this work we study the inverse scattering problem for the selfadjoint
matrix Schrodinger operator on the half line. We provide the necessary and
sufficient conditions for the solvability of the inverse scattering problem.Comment: 29 page
Inverse resonance problems for the Schroedinger operator on the real line with mixed given data
In this work, we study inverse resonance problems for the Schr\"odinger
operator on the real line with the potential supported in . In general,
all eigenvalues and resonances can not uniquely determine the potential. (i) It
is shown that if the potential is known a priori on , then the unique
recovery of the potential on the whole interval from all eigenvalues and
resonances is valid. (ii) If the potential is known a priori on , then
for the case , infinitely many eigenvalues and resonances can be missing
for the unique determination of the potential, and for the case , all
eigenvalues and resonances plus a part of so-called sign-set can uniquely
determine the potential. (iii) It is also shown that all eigenvalues and
resonances, together with a set of logarithmic derivative values of
eigenfunctions and wave-functions at , can uniquely determine the
potential.Comment: 12 page
The diffuse gamma-ray flux associated with sub-PeV/PeV neutrinos from starburst galaxies
One attractive scenario for the excess of sub-PeV/PeV neutrinos recently
reported by IceCube is that they are produced by cosmic rays in starburst
galaxies colliding with the dense interstellar medium. These proton-proton
() collisions also produce high-energy gamma-rays, which finally contribute
to the diffuse high-energy gamma-ray background. We calculate the diffuse
gamma-ray flux with a semi-analytic approach and consider that the very high
energy gamma-rays will be absorbed in the galaxies and converted into
electron-position pairs, which then lose almost all their energy through
synchrotron radiation in the strong magnetic fields in the starburst region.
Since the synchrotron emission goes into energies below GeV, this synchrotron
loss reduces the diffuse high-energy gamma-ray flux by a factor of about two,
thus leaving more room for other sources to contribute to the gamma-ray
background. For a neutrino spectrum, we find that the diffuse
gamma-ray flux contributes about 20% of the observed diffuse gamma-ray
background in the 100 GeV range. However, for a steeper neutrino spectrum, this
synchrotron loss effect is less important, since the energy fraction in
absorbed gamma-rays becomes lower.Comment: Accepted by ApJ, one figure added, small revisions in text, results
and conclusions unchange
Indecomposability of entanglement witnesses constructed from any permutations
Let and be a linear map defined by
,
where , s are the matrix units and is a
non-identity permutation of . Denote by the set of all minimal cycles of and the length of . It is shown that the Hermitian matrix
induced by is an indecomposable entanglement
witness if and only if (the identity permutation) and
. Some new bounded entangled states are detected by
such witnesses that cannot be distinguished by PPT criterion, realignment
criterion, etc..Comment: 11 page
A parallel space-time domain decomposition method for unsteady source inversion problems
In this paper, we propose a parallel space-time domain decomposition method
for solving an unsteady source identification problem governed by the linear
convection-diffusion equation. Traditional approaches require to solve
repeatedly a forward parabolic system, an adjoint system and a system with
respect to the unknowns. The three systems have to be solved one after another.
These sequential steps are not desirable for large scale parallel computing. A
space-time restrictive additive Schwarz method is proposed for a fully implicit
space-time coupled discretization scheme to recover the time-dependent
pollutant source intensity functions. We show with numerical experiments that
the scheme works well with noise in the observation data. More importantly it
is demonstrated that the parallel space-time Schwarz preconditioner is scalable
on a supercomputer with over processors, thus promising for large scale
applications
Distinguishing the right-handed up/charm quarks from top quark via discrete symmetries in the standard model extensions
We propose a class of the two Higgs doublet Standard models (SMs) with a SM
singlet and a class of supersymmetric SMs with two pairs of Higgs doublets,
where the right-handed up/charm quarks and the right-handed top quark have
different quantum numbers under extra discrete symmetries. Thus, the
right-handed up and charm quarks couple to one Higgs doublet field, while the
right-handed top quark couples to another Higgs doublet. The quark CKM mixings
can be generated from the down-type quark sector. As one of phenomenological
consequences in our models, we explore whether one can accommodate the observed
direct CP asymmetry difference in singly Cabibbo-suppressed D decays. We show
that it is possible to explain the measured values of CP violation under
relevant experimental constraints.Comment: 20 pages; matches published versio
Two-level space-time domain decomposition methods for unsteady inverse problems
As the number of processor cores on supercomputers becomes larger and larger,
algorithms with high degree of parallelism attract more attention. In this
work, we propose a novel space-time coupled algorithm for solving an inverse
problem associated with the time-dependent convection-diffusion equation in
three dimensions. We introduce a mixed finite element/finite difference method
and a one-level and a two-level space-time parallel domain decomposition
preconditioner for the Karush-Kuhn-Tucker (KKT) system induced from
reformulating the inverse problem as an output least-squares optimization
problem in the space-time domain. The new full space approach eliminates the
sequential steps of the optimization outer loop and the inner forward and
backward time marching processes, thus achieves high degree of parallelism.
Numerical experiments validate that this approach is effective and robust for
recovering unsteady moving sources. We report strong scalability results
obtained on a supercomputer with more than 1,000 processors
The Super-Natural Supersymmetry and Its Classic Example: M-Theory Inspired NMSSM
We briefly review the super-natural supersymmetry (SUSY), which provides a
most promising solution to the SUSY electroweak fine-tuning problem. In
particular, we address its subtle issues as well. Unlike the Minimal
Supersymmetric Standard model (MSSM), the Next to MSSM (NMSSM) can be scale
invariant and has no mass parameter in its Lagrangian before SUSY and gauge
symmetry breakings. Therefore, the NMSSM is a perfect framework for
super-natural SUSY. To give the SUSY breaking soft mass to the singlet, we
consider the moduli and dilaton dominant SUSY breaking scenarios in M-theory on
. In these scenarios, SUSY is broken by one and only one -term of
moduli or dilaton, and the SUSY breaking soft terms can be determined via the
K\"ahler potential and superpotential from Calabi-Yau compactification of
M-theory on . Thus, as predicted by super-natural SUSY, the SUSY
electroweak fine-tuning measure is of unity order. In the moduli dominant SUSY
breaking scenario, the right-handed sleptons are relatively light around 1 TeV,
stau can be even as light as 580 GeV and degenerate with the lightest
neutralino, chargino masses are larger than 1 TeV, the light stop masses are
around 2 TeV or larger, the first two-generation squark masses are about 3 TeV
or larger, and gluinos are heavier than squarks. In the dilaton dominant SUSY
breaking scenario, the qualitative picture remain the same but we have heavier
spectra as compared to moduli dominant SUSY breaking scenario. In addition to
it, we have Higgs -resonance solutions for dark matter (DM). In
both scenarios, the minimal value of DM relic density is about 0.2. To obtain
the observed DM relic density, we can consider the dilution effect from
supercritical string cosmology or introduce the axino as the lightest
supersymmetric particle.Comment: 35 pages, 12 figures and two table
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