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 $SU(2) \times SU(2)$. 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

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 $p_\eta$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_\eta$. 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