254,374 research outputs found
Dimensional Reduction via Noncommutative Spacetime: Bootstrap and Holography
Unlike noncommutative space, when space and time are noncommutative, it seems
necessary to modify the usual scheme of quantum mechanics. We propose in this
paper a simple generalization of the time evolution equation in quantum
mechanics to incorporate the feature of a noncommutative spacetime. This
equation is much more constraining than the usual Schr\"odinger equation in
that the spatial dimension noncommuting with time is effectively reduced to a
point in low energy. We thus call the new evolution equation the spacetime
bootstrap equation, the dimensional reduction called for by this evolution
seems close to what is required by the holographic principle. We will discuss
several examples to demonstrate this point.Comment: 15 pages, harvmac. v2: typos corrected and some changes mad
Photoproduction of Pentaquark in Feynman and Regge Theories
Photoproduction of the Theta+ pentaquark on the proton is analyzed by using
an isobar and a Regge models. The difference in the calculated total cross
section is found to be more than two orders of magnitude for a hadronic form
factor cut-off Lambda > 1 GeV. Comparable results would be obtained for 0.6 <
Lambda < 0.8 GeV. We also calculate contribution of the Theta+ photoproduction
to the GDH integral. By comparing with the current phenomenological
calculation, it is found that the GDH sum rule favors the result obtained from
Regge approach and isobar model with small Lambda.Comment: 5 pages, 5 figures, submitted to Phys.Rev.C as a Rapid Communicatio
Temporal variability in early afterglows of short gamma-ray bursts
The shock model has successfully explained the observed behaviors of
afterglows from long gamma-ray bursts (GRBs). Here we use it to investigate the
so-called early afterglows from short GRBs, which arises from blast waves that
are not decelerated considerably by their surrounding medium. We consider a
nearby medium loaded with pairs (Beloborodov 2002). The temporal
behaviors show first a soft-to-hard spectral evolution, from the optical to
hard X-ray, and then a usual hard-to-soft evolution after the blast waves begin
to decelerate. The light curves show variability, and consist of two peaks. The
first peak, due to the pair effect, can be observed in the X-ray, though too
faint and too short in the optical. The second peak will be easily detected by
{\it Swift}. We show that detections of the double-peak structure in the light
curves of early afterglows are very helpful to determine all the shock
parameters of short GRBs, including both the parameters of the relativistic
source and the surroundings. Besides, from the requirement that the
forward-shock emission in short GRBs should be below the BATSE detection
threshold, we give a strong constraint on the shock model parameters. In
particular, the initial Lorentz factor of the source is limited to be no more
than , and the ambient medium density is inferred to be low, n\la
10^{-1} cm.Comment: 5 pages, 1 figure, minor changes to match the publish in MNRA
Convergence of the Lasserre Hierarchy of SDP Relaxations for Convex Polynomial Programs without Compactness
The Lasserre hierarchy of semidefinite programming (SDP) relaxations is an
effective scheme for finding computationally feasible SDP approximations of
polynomial optimization over compact semi-algebraic sets. In this paper, we
show that, for convex polynomial optimization, the Lasserre hierarchy with a
slightly extended quadratic module always converges asymptotically even in the
face of non-compact semi-algebraic feasible sets. We do this by exploiting a
coercivity property of convex polynomials that are bounded below. We further
establish that the positive definiteness of the Hessian of the associated
Lagrangian at a saddle-point (rather than the objective function at each
minimizer) guarantees finite convergence of the hierarchy. We obtain finite
convergence by first establishing a new sum-of-squares polynomial
representation of convex polynomials over convex semi-algebraic sets under a
saddle-point condition. We finally prove that the existence of a saddle-point
of the Lagrangian for a convex polynomial program is also necessary for the
hierarchy to have finite convergence.Comment: 17 page
A Two-Tiered Correlation of Dark Matter with Missing Transverse Energy: Reconstructing the Lightest Supersymmetric Particle Mass at the LHC
We suggest that non-trivial correlations between the dark matter particle
mass and collider based probes of missing transverse energy H_T^miss may
facilitate a two tiered approach to the initial discovery of supersymmetry and
the subsequent reconstruction of the LSP mass at the LHC. These correlations
are demonstrated via extensive Monte Carlo simulation of seventeen benchmark
models, each sampled at five distinct LHC center-of-mass beam energies,
spanning the parameter space of No-Scale F-SU(5).This construction is defined
in turn by the union of the Flipped SU(5) Grand Unified Theory, two pairs of
hypothetical TeV scale vector-like supersymmetric multiplets with origins in
F-theory, and the dynamically established boundary conditions of No-Scale
Supergravity. In addition, we consider a control sample comprised of a standard
minimal Supergravity benchmark point. Led by a striking similarity between the
H_T^miss distribution and the familiar power spectrum of a black body radiator
at various temperatures, we implement a broad empirical fit of our simulation
against a Poisson distribution ansatz. We advance the resulting fit as a
theoretical blueprint for deducing the mass of the LSP, utilizing only the
missing transverse energy in a statistical sampling of >= 9 jet events.
Cumulative uncertainties central to the method subsist at a satisfactory 12-15%
level. The fact that supersymmetric particle spectrum of No-Scale F-SU(5) has
thrived the withering onslaught of early LHC data that is steadily decimating
the Constrained Minimal Supersymmetric Standard Model and minimal Supergravity
parameter spaces is a prime motivation for augmenting more conventional LSP
search methodologies with the presently proposed alternative.Comment: JHEP version, 17 pages, 9 Figures, 2 Table
Spontaneous and Superfluid Chiral Edge States in Exciton-Polariton Condensates
We present a scheme of interaction-induced topological bandstructures based
on the spin anisotropy of exciton-polaritons in semiconductor microcavities. We
predict theoretically that this scheme allows the engineering of topological
gaps, without requiring a magnetic field or strong spin-orbit interaction
(transverse electric-transverse magnetic splitting). Under non-resonant
pumping, we find that an initially topologically trivial system undergoes a
topological transition upon the spontaneous breaking of phase symmetry
associated with polariton condensation. Under resonant coherent pumping, we
find that it is also possible to engineer a topological dispersion that is
linear in wavevector -- a property associated with polariton superfluidity.Comment: 6 pages, 4 figure
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