7,541 research outputs found
Massless Scalar Field Propagator in a Quantized Space-Time
We consider in detail the analytic behaviour of the non-interacting massless
scalar field two-point function in H.S. Snyder's discretized non-commuting
spacetime. The propagator we find is purely real on the Euclidean side of the
complex plane and goes like as from either the
Euclidean or Minkowski side. The real part of the propagator goes smoothly to
zero as increases to the discretization scale and remains zero
for . This behaviour is consistent with the termination of
single-particle propagation on the ultraviolet side of the discretization
scale. The imaginary part of the propagator, consistent with a
multiparticle-production branch discontinuity, is finite and continuous on the
Minkowski side, slowly falling to zero when . Finally, we
argue that the spectral function for the multiparticle states appears to
saturate as probes just beyond the discretization scale. We
speculate on the cosmological consequences of such a spectral function.Comment: 6 pages, 1 eps figure embedded in manuscrip
Imaging Transport Resonances in the Quantum Hall Effect
We use a scanning capacitance probe to image transport in the quantum Hall
system. Applying a DC bias voltage to the tip induces a ring-shaped
incompressible strip (IS) in the 2D electron system (2DES) that moves with the
tip. At certain tip positions, short-range disorder in the 2DES creates a
quantum dot island in the IS. These islands enable resonant tunneling across
the IS, enhancing its conductance by more than four orders of magnitude. The
images provide a quantitative measure of disorder and suggest resonant
tunneling as the primary mechanism for transport across ISs.Comment: 4 pages, 4 figures, submitted to PRL. For movies and additional
infomation, see http://electron.mit.edu/scanning/; Added scale bars to
images, revised discussion of figure 3, other minor change
Optimal Renormalization-Group Improvement of R(s) via the Method of Characteristics
We discuss the application of the method of characteristics to the
renormalization-group equation for the perturbative QCD series within the
electron-positron annihilation cross-section. We demonstrate how one such
renormalization-group improvement of this series is equivalent to a closed-form
summation of the first four towers of renormalization-group accessible
logarithms to all orders of perturbation theory
Can the Renormalization Group Improved Effective Potential be used to estimate the Higgs Mass in the Conformal Limit of the Standard Model?
We consider the effective potential in the standard model with a single
Higgs doublet in the limit that the only mass scale present is
radiatively generated. Using a technique that has been shown to determine
completely in terms of the renormalization group (RG) functions when using the
Coleman-Weinberg (CW) renormalization scheme, we first sum leading-log (LL)
contributions to using the one loop RG functions, associated with five
couplings (the top quark Yukawa coupling , the quartic coupling of the Higgs
field , the SU(3) gauge coupling , and the couplings
and ). We then employ the two loop RG functions with the three couplings
, , to sum the next-to-leading-log (NLL) contributions to and
then the three to five loop RG functions with one coupling to sum all the
contributions to . In order to compute these sums, it is
necessary to convert those RG functions that have been originally computed
explicitly in the minimal subtraction (MS) scheme to their form in the CW
scheme. The Higgs mass can then be determined from the effective potential: the
result is decreases to at
order and at order. No reasonable
estimate of can be made at orders or . This is taken
to be an indication that this mechanism for spontaneous symmetry breaking is in
fact viable, though one in which there is slow convergence towards the actual
value of . The mass is argued to be an upper bound on
.Comment: 24 pages, 5 figures. Updated version contains new discussion,
references, figures, and corrects errors in reference
Constraints on Higher-Order Perturbative Corrections in Semileptonic Decays from Residual Renormalization-Scale Dependence
The constraint of a progressive decrease in residual renormalization scale
dependence with increasing loop order is developed as a method for obtaining
bounds on unknown higher-order perturbative corrections to
renormalization-group invariant quantities. This technique is applied to the
inclusive semileptonic process (explicitly known to
two-loop order) to obtain bounds on the three- and four-loop perturbative
coefficients that are not accessible via the renormalization group. Using the
principle of minimal sensitivity, an estimate is obtained for the perturbative
contributions to that incorporates
theoretical uncertainty from as-yet-undetermined higher order QCD corrections.Comment: latex2e using amsmath, 8 pages, 4 embedded eps figures. Revised
version contains an additional figure and accompanying revision
Oseledets' Splitting of Standard-like Maps
For the class of differentiable maps of the plane and, in particular, for
standard-like maps (McMillan form), a simple relation is shown between the
directions of the local invariant manifolds of a generic point and its
contribution to the finite-time Lyapunov exponents (FTLE) of the associated
orbit. By computing also the point-wise curvature of the manifolds, we produce
a comparative study between local Lyapunov exponent, manifold's curvature and
splitting angle between stable/unstable manifolds. Interestingly, the analysis
of the Chirikov-Taylor standard map suggests that the positive contributions to
the FTLE average mostly come from points of the orbit where the structure of
the manifolds is locally hyperbolic: where the manifolds are flat and
transversal, the one-step exponent is predominantly positive and large; this
behaviour is intended in a purely statistical sense, since it exhibits large
deviations. Such phenomenon can be understood by analytic arguments which, as a
by-product, also suggest an explicit way to point-wise approximate the
splitting.Comment: 17 pages, 11 figure
The Automatic Real-Time GRB Pipeline of the 2-m Liverpool Telescope
The 2-m Liverpool Telescope (LT), owned by Liverpool John Moores University,
is located in La Palma (Canary Islands) and operates in fully robotic mode. In
2005, the LT began conducting an automatic GRB follow-up program. On receiving
an automatic GRB alert from a Gamma-Ray Observatory (Swift, INTEGRAL, HETE-II,
IPN) the LT initiates a special override mode that conducts follow-up
observations within 2-3 min of the GRB onset. This follow-up procedure begins
with an initial sequence of short (10-s) exposures acquired through an r' band
filter. These images are reduced, analyzed and interpreted automatically using
pipeline software developed by our team called "LT-TRAP" (Liverpool Telescope
Transient Rapid Analysis Pipeline); the automatic detection and successful
identification of an unknown and potentially fading optical transient triggers
a subsequent multi-color imaging sequence. In the case of a candidate brighter
than r'=15, either a polarimetric (from 2006) or a spectroscopic observation
(from 2007) will be triggered on the LT. If no candidate is identified, the
telescope continues to obtain z', r' and i' band imaging with increasingly
longer exposure times. Here we present a detailed description of the LT-TRAP
and briefly discuss the illustrative case of the afterglow of GRB 050502a,
whose automatic identification by the LT just 3 min after the GRB, led to the
acquisition of the first early-time (< 1 hr) multi-color light curve of a GRB
afterglow.Comment: PASP, accepted (8 pages, 3 figures
An ingress and a complete transit of HD 80606 b
We have used four telescopes at different longitudes to obtain
near-continuous lightcurve coverage of the star HD 80606 as it was transited by
its \sim 4-MJup planet. The observations were performed during the predicted
transit windows around the 25th of October 2008 and the 14th of February 2009.
Our data set is unique in that it simultaneously constrains the duration of the
transit and the planet's period. Our Markov-Chain Monte Carlo analysis of the
light curves, combined with constraints from radial-velocity data, yields
system parameters consistent with previously reported values. We find a
planet-to-star radius ratio marginally smaller than previously reported,
corresponding to a planet radius of Rp = 0.921 \pm 0.036RJup .Comment: 6 pages, 2 figures, MNRAS accepte
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