14,923 research outputs found
Large Fourier transforms never exactly realized by braiding conformal blocks
Fourier transform is an essential ingredient in Shor's factoring algorithm.
In the standard quantum circuit model with the gate set \{\U(2),
\textrm{CNOT}\}, the discrete Fourier transforms , can be realized exactly by
quantum circuits of size , and so can the discrete
sine/cosine transforms. In topological quantum computing, the simplest
universal topological quantum computer is based on the Fibonacci
(2+1)-topological quantum field theory (TQFT), where the standard quantum
circuits are replaced by unitary transformations realized by braiding conformal
blocks. We report here that the large Fourier transforms and the discrete
sine/cosine transforms can never be realized exactly by braiding conformal
blocks for a fixed TQFT. It follows that approximation is unavoidable to
implement the Fourier transforms by braiding conformal blocks
A first-order Green's function approach to supersonic oscillatory flow: A mixed analytic and numeric treatment
A frequency domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. In this range the effects of the nonlinear terms in the unsteady supersonic compressible velocity potential equation are negligible and therefore these terms will be omitted. The Green's function method is employed in order to convert the potential flow differential equation into an integral one. This integral equation is then discretized, through standard finite element technique, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration (e.g., finite-thickness wing, wing-body-tail) is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. The long range goal is to develop a comprehensive theory for unsteady supersonic potential aerodynamic which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range
Atmospheric Sulfur Photochemistry on Hot Jupiters
We develop a new 1D photochemical kinetics code to address stratospheric
chemistry and stratospheric heating in hot Jupiters. Here we address optically
active S-containing species and CO2 at 1200 < T < 2000 K. HS (mercapto) and S2
are highly reactive species that are generated photochemically and
thermochemically from H2S with peak abundances between 1-10 mbar. S2 absorbs UV
between 240 and 340 nm and is optically thick for metallicities [SH] > 0 at T >
1200 K. HS is probably more important than S2, as it is generally more abundant
than S2 under hot Jupiter conditions and it absorbs at somewhat redder
wavelengths. We use molecular theory to compute an HS absorption spectrum from
sparse available data and find that HS should absorb strongly between 300 and
460 nm, with absorption at the longer wavelengths being temperature sensitive.
When the two absorbers are combined, radiative heating (per kg of gas) peaks at
100 microbars, with a total stratospheric heating of about 8 x 10^4 W/m^2 for a
jovian planet orbiting a solar-twin at 0.032 AU. Total heating is insensitive
to metallicity. The CO2 mixing ratio is a well-behaved quadratic function of
metallicity, ranging from 1.6 x 10^-8 to 1.6 x 10^-4 for -0.3 < [M/H] < 1.7.
CO2 is insensitive to insolation, vertical mixing, temperature (1200 < T <2000
K), and gravity. The photochemical calculations confirm that CO2 should prove a
useful probe of planetary metallicity.Comment: Astrophysical Journal Lett. in press; important revision includes
effect of updated thermodynamic data and a new opacity sourc
From Soft Walls to Infrared Branes
Five dimensional warped spaces with soft walls are generalizations of the
standard Randall-Sundrum compactifications, where instead of an infrared brane
one has a curvature singularity (with vanishing warp factor) at finite proper
distance in the bulk. We project the physics near the singularity onto a
hypersurface located a small distance away from it in the bulk. This results in
a completely equivalent description of the soft wall in terms of an effective
infrared brane, hiding any singular point. We perform explicitly this
calculation for two classes of soft wall backgrounds used in the literature.
The procedure has several advantages. It separates in a clean way the physics
of the soft wall from the physics of the five dimensional bulk, facilitating a
more direct comparison with standard two-brane warped compactifications.
Moreover, consistent soft walls show a sort of universal behavior near the
singularity which is reflected in the effective brane Lagrangian. Thirdly, for
many purposes, a good approximation is obtained by assuming the bulk background
away from the singularity to be the usual Randall-Sundrum metric, thus making
the soft wall backgrounds better analytically tractable. We check the validity
of this procedure by calculating the spectrum of bulk fields and comparing it
to the exact result, finding very good agreement.Comment: 14 pages, 2 figures, v2: subsection on IR brane potentials and
appendix on fermions added, version to appear in PR
SU(m) non-Abelian anyons in the Jain hierarchy of quantum Hall states
We show that different classes of topological order can be distinguished by
the dynamical symmetry algebra of edge excitations. Fundamental topological
order is realized when this algebra is the largest possible, the algebra of
quantum area-preserving diffeomorphisms, called . We argue that
this order is realized in the Jain hierarchy of fractional quantum Hall states
and show that it is more robust than the standard Abelian Chern-Simons order
since it has a lower entanglement entropy due to the non-Abelian character of
the quasi-particle anyon excitations. These behave as SU() quarks, where
is the number of components in the hierarchy. We propose the topological
entanglement entropy as the experimental measure to detect the existence of
these quantum Hall quarks. Non-Abelian anyons in the fractional
quantum Hall states could be the primary candidates to realize qbits for
topological quantum computation.Comment: 5 pages, no figures, a few typos corrected, a reference adde
Supersymmetry algebra in N = 1 chiral supergravity
We consider the supersymmetry (SUSY) transformations in the chiral Lagrangian
for supergravity (SUGRA) with the complex tetrad following the method
used in the usual SUGRA, and present the explicit form of the SUSY
trasformations in the first-order form. The SUSY transformations are generated
by two independent Majorana spinor parameters, which are apparently different
from the constrained parameters employed in the method of the 2-form gravity.
We also calculate the commutator algebra of the SUSY transformations on-shell.Comment: 10 pages, late
A Unified Theory for the Atmospheres of the Hot and Very Hot Jupiters: Two Classes of Irradiated Atmospheres
We highlight the importance of gaseous TiO and VO opacity on the highly
irradiated close-in giant planets. The atmospheres of these planets naturally
fall into two classes that are somewhat analogous to the M- and L-type dwarfs.
Those that are warm enough to have appreciable opacity due to TiO and VO gases
we term the ``pM Class'' planets, and those that are cooler we term ``pL
Class'' planets. We calculate model atmospheres for these planets, including
pressure-temperature profiles, spectra, and characteristic radiative time
constants. We show that pM Class planets have hot stratospheres 2000 K
and appear ``anomalously'' bright in the mid infrared secondary eclipse, as was
recently found for planets HD 149026b and HD 209458b. This class of planets
absorbs incident flux and emits thermal flux from high in their atmospheres.
Consequently, they will have large day/night temperature contrasts and
negligible phase shifts between orbital phase and thermal emission light
curves, because radiative timescales are much shorter than possible dynamical
timescales. The pL Class planets absorb incident flux deeper in the atmosphere
where atmospheric dynamics will more readily redistribute absorbed energy. This
will lead to cooler day sides, warmer night sides, and larger phase shifts in
thermal emission light curves. Around a Sun-like primary this boundary occurs
at 0.04-0.05 AU. The eccentric transiting planets HD 147506b and HD
17156b alternate between the classes. Thermal emission in the optical from pM
Class planets is significant red-ward of 400 nm, making these planets
attractive targets for optical detection. The difference in the observed
day/night contrast between ups Andromeda b (pM Class) and HD 189733b (pL Class)
is naturally explained in this scenario. (Abridged.)Comment: Accepted to the Astrophysical Journa
Holographic Normal Ordering and Multi-particle States in the AdS/CFT Correspondence
The general correlator of composite operators of N=4 supersymmetric gauge
field theory is divergent. We introduce a means for renormalizing these
correlators by adding a boundary theory on the AdS space correcting for the
divergences. Such renormalizations are not equivalent to the standard normal
ordering of current algebras in two dimensions. The correlators contain contact
terms that contribute to the OPE; we relate them diagrammatically to
correlation functions of compound composite operators dual to multi-particle
states.Comment: 18 pages, one equation corr., further comments and refs. adde
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