6,651 research outputs found
Chow's theorem and universal holonomic quantum computation
A theorem from control theory relating the Lie algebra generated by vector
fields on a manifold to the controllability of the dynamical system is shown to
apply to Holonomic Quantum Computation. Conditions for deriving the holonomy
algebra are presented by taking covariant derivatives of the curvature
associated to a non-Abelian gauge connection. When applied to the Optical
Holonomic Computer, these conditions determine that the holonomy group of the
two-qubit interaction model contains . In particular, a
universal two-qubit logic gate is attainable for this model.Comment: 13 page
Geometric phases and anholonomy for a class of chaotic classical systems
Berry's phase may be viewed as arising from the parallel transport of a
quantal state around a loop in parameter space. In this Letter, the classical
limit of this transport is obtained for a particular class of chaotic systems.
It is shown that this ``classical parallel transport'' is anholonomic ---
transport around a closed curve in parameter space does not bring a point in
phase space back to itself --- and is intimately related to the Robbins-Berry
classical two-form.Comment: Revtex, 11 pages, no figures
Optimal control, geometry, and quantum computing
We prove upper and lower bounds relating the quantum gate complexity of a
unitary operation, U, to the optimal control cost associated to the synthesis
of U. These bounds apply for any optimal control problem, and can be used to
show that the quantum gate complexity is essentially equivalent to the optimal
control cost for a wide range of problems, including time-optimal control and
finding minimal distances on certain Riemannian, subriemannian, and Finslerian
manifolds. These results generalize the results of Nielsen, Dowling, Gu, and
Doherty, Science 311, 1133-1135 (2006), which showed that the gate complexity
can be related to distances on a Riemannian manifoldComment: 7 Pages Added Full Names to Author
Positive and negative regulatory regions control the spatial distribution of polygalacturonase transcription in tomato fruit pericarp.
Velocity field distributions due to ideal line vortices
We evaluate numerically the velocity field distributions produced by a
bounded, two-dimensional fluid model consisting of a collection of parallel
ideal line vortices. We sample at many spatial points inside a rigid circular
boundary. We focus on ``nearest neighbor'' contributions that result from
vortices that fall (randomly) very close to the spatial points where the
velocity is being sampled. We confirm that these events lead to a non-Gaussian
high-velocity ``tail'' on an otherwise Gaussian distribution function for the
Eulerian velocity field. We also investigate the behavior of distributions that
do not have equilibrium mean-field probability distributions that are uniform
inside the circle, but instead correspond to both higher and lower mean-field
energies than those associated with the uniform vorticity distribution. We find
substantial differences between these and the uniform case.Comment: 21 pages, 9 figures. To be published in Physical Review E
(http://pre.aps.org/) in May 200
Report on Sediment Transport Events on Shelf and Slope (STRESS) field season 1 : Winter 1988-1989 Benthic Acoustic Stress Sensor (BASS)
Data on the effects of winter conditions on the transport of sediment on the continental shelf off Northern California were
collected during the flrst year of the Sediment TRansport Events on Shelf and Slope (STRESS) Experiment. This experiment was
done in conjunction with (Shelf Mixed Layer Experiment) SMILE and (Biological Effects on Coastal Ocean Sediment Transport)
BECOST to provide a complete suite of measurements of nearshore dynamics, sediment transport, and biological interactions.
This report includes a general description of the work accomplished during the frrst STRESS fleld season, carried out in the
winter of 1988-1989 off the Northern California coast Three cruises were completed during the STRESS experiment, one each for
deployment, turnaround, and r~overy of the instruments. This created two back-to-back sections of data, one from December 4,
1988 to January 23, 1989, and the other from January 29 to March 17, 1989.
This report also documents in detail the use of the Benthic Acoustic Stress Sensor (BASS), and the associated acoustic data
telemetry link in STRESS. BASS has been used in different configurations previously, but the acoustic telemetry system is new.Funding was provided by the Office of Naval Research
under Contract No. N000-14-89-J-105
The Quantum Mellin transform
We uncover a new type of unitary operation for quantum mechanics on the
half-line which yields a transformation to ``Hyperbolic phase space''. We show
that this new unitary change of basis from the position x on the half line to
the Hyperbolic momentum , transforms the wavefunction via a Mellin
transform on to the critial line . We utilise this new transform
to find quantum wavefunctions whose Hyperbolic momentum representation
approximate a class of higher transcendental functions, and in particular,
approximate the Riemann Zeta function. We finally give possible physical
realisations to perform an indirect measurement of the Hyperbolic momentum of a
quantum system on the half-line.Comment: 23 pages, 6 Figure
Darwin Tames an Andromeda Dwarf: Unraveling the Orbit of NGC 205 Using a Genetic Algorithm
NGC 205, a close satellite of the M31 galaxy, is our nearest example of a
dwarf elliptical galaxy. Photometric and kinematic observations suggest that
NGC 205 is undergoing tidal distortion from its interaction with M31. Despite
earlier attempts, the orbit and progenitor properties of NGC 205 are not well
known. We perform an optimized search for these unknowns by combining a genetic
algorithm with restricted N-body simulations of the interaction. This approach,
coupled with photometric and kinematic observations as constraints, allows for
an effective exploration of the parameter space. We represent NGC 205 as a
static Hernquist potential with embedded massless test particles that serve as
tracers of surface brightness. We explore 3 distinct, initially stable
configurations of test particles: cold rotating disk, warm rotating disk, and
hot, pressure-supported spheroid. Each model reproduces some, but not all, of
the observed features of NGC 205, leading us to speculate that a rotating
progenitor with substantial pressure support could match all of the
observables. Furthermore, plausible combinations of mass and scale length for
the pressure-supported spheroid progenitor model reproduce the observed
velocity dispersion profile. For all 3 models, orbits that best match the
observables place the satellite 11+/-9 kpc behind M31 moving at very large
velocities: 300-500 km/s on primarily radial orbits. Given that the observed
radial component is only 54 km/s, this implies a large tangential motion for
NGC 205, moving from the NW to the SE. These results suggest NGC 205 is not
associated with the stellar arc observed to the NE of NGC 205. Furthermore, NGC
205's velocity appears to be near or greater than its escape velocity,
signifying that the satellite is likely on its first M31 passage.Comment: 34 pages, 20 figures, accepted for publication in the Astrophysical
Journal, A pdf version with high-resolution figures may be obtained from
http://www.ucolick.org/~kirsten/ms.pd
On the notion of phase in mechanics
The notion of phase plays an esential role in both classical and quantum
mechanics.But what is a phase? We show that if we define the notion of phase in
phase (!) space one can very easily and naturally recover the Heisenberg-Weyl
formalism; this is achieved using the properties of the Poincare-Cartan
invariant, and without making any quantum assumption
Reconstructing Dryopteris “semicristata” (Dryopteridaceae): Molecular profiles of tetraploids verify their undiscovered diploid ancestor
This is the publisher's version, also available electronically from http://www.amjbot.org.• Premise of the study: Discovering missing ancestors is essential to understanding the evolutionary history of biodiversity on Earth. Evidence from extinct species can provide links for reconstructing intricate patterns of reticulate relationships among extant descendents. When fossils are unavailable and other evidence yields competing hypotheses to explain species ancestry, data from proteins and DNA can help resolve conflicts and generate novel perspectives. The identity of a parent shared by two tetraploid species in the cosmopolitan fern genus Dryopteris has remained elusive for more than 50 years. Based on available data, four hypotheses were developed previously, each providing a different resolution to this uncertainty.
• Methods: New molecular evidence from studies of isozymes and restriction site analysis of chloroplast DNA tested the competing hypotheses about the diploid ancestors of these two extant Dryopteris polyploids.
• Key results: The results falsify two of the hypotheses, resolve the uncertainty in the third, and support the fourth.
• Conclusions: Our data validate the prior existence of Dryopteris “semicristata,” which was proposed 38 years ago as a diploid progenitor of the allotetraploids D. cristata and D. carthusiana but has never been collected. After developing a phylogeny using the new molecular data, we describe a plausible morphology for D. “semicristata” by extrapolating likely character states from related extant species
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