435 research outputs found
Bundle Theory of Improper Spin Transformations
{\it We first give a geometrical description of the action of the parity
operator () on non relativistic spin Pauli spinors in
terms of bundle theory. The relevant bundle, , is a
non trivial extension of the universal covering group .
is the non relativistic limit of the corresponding Dirac matrix
operator and obeys . Then, from the direct
product of O(3) by , naturally induced by the structure of the galilean
group, we identify, in its double cover, the time reversal operator ()
acting on spinors, and its product with . Both, and
, generate the group . As in the case of parity,
is the non relativistic limit of the corresponding Dirac matrix
operator , and obeys .}Comment: 8 pages, Plaintex; titled changed, minor text modifications, one
reference complete
The geometry of entanglement: metrics, connections and the geometric phase
Using the natural connection equivalent to the SU(2) Yang-Mills instanton on
the quaternionic Hopf fibration of over the quaternionic projective space
with an fiber the geometry of
entanglement for two qubits is investigated. The relationship between base and
fiber i.e. the twisting of the bundle corresponds to the entanglement of the
qubits. The measure of entanglement can be related to the length of the
shortest geodesic with respect to the Mannoury-Fubini-Study metric on between an arbitrary entangled state, and the separable state nearest to
it. Using this result an interpretation of the standard Schmidt decomposition
in geometric terms is given. Schmidt states are the nearest and furthest
separable ones lying on, or the ones obtained by parallel transport along the
geodesic passing through the entangled state. Some examples showing the
correspondence between the anolonomy of the connection and entanglement via the
geometric phase is shown. Connections with important notions like the
Bures-metric, Uhlmann's connection, the hyperbolic structure for density
matrices and anholonomic quantum computation are also pointed out.Comment: 42 page
Impurity and quaternions in nonrelativistic scattering from a quantum memory
Models of quantum computing rely on transformations of the states of a
quantum memory. We study mathematical aspects of a model proposed by Wu in
which the memory state is changed via the scattering of incoming particles.
This operation causes the memory content to deviate from a pure state, i.e.
induces impurity. For nonrelativistic particles scattered from a two-state
memory and sufficiently general interaction potentials in 1+1 dimensions, we
express impurity in terms of quaternionic commutators. In this context, pure
memory states correspond to null hyperbolic quaternions. In the case with point
interactions, the scattering process amounts to appropriate rotations of
quaternions in the frequency domain. Our work complements a previous analysis
by Margetis and Myers (2006 J. Phys. A 39 11567--11581).Comment: 16 pages, no figure
Limits on Stellar and Planetary Companions in Microlensing Event OGLE-1998-BUL-14
We present the PLANET photometric data set for \ob14, a high magnification
() event alerted by the OGLE collaboration toward the
Galactic bulge in 1998. The PLANET data set consists a total of 461 I-band and
139 band points, the majority of which was taken over a three month period.
The median sampling interval during this period is about 1 hour, and the
scatter over the peak of the event is 1.5%. The excellent data
quality and high maximum magnification of this event make it a prime candidate
to search for the short duration, low amplitude perturbations that are
signatures of a planetary companion orbiting the primary lens. The observed
light curve for \ob14 is consistent with a single lens (no companion) within
photometric uncertainties. We calculate the detection efficiency of the light
curve to lensing companions as a function of the mass ratio and angular
separation of the two components. We find that companions of mass ratio are ruled out at the 95% confidence level for projected separations
between 0.4-2.4 \re, where \re is the Einstein ring radius of the primary
lens. Assuming that the primary is a G-dwarf with \re\sim3 {\rm AU} our
detection efficiency for this event is for a companion with the mass
and separation of Jupiter and for a companion with the mass and
separation of Saturn. Our efficiencies for planets like those around Upsilon
And and 14 Her are > 75%.Comment: Data available at http://www.astro.rug.nl/~planet/planetpapers.html
20 pages, 10 figures. Minor changes. ApJ, accepte
A Complete Set of Solutions For Caustic-Crossing Binary Microlensing Events
We present a method to analyze binary-lens microlensing light curves with one
well-sampled fold caustic crossing. In general, the surface of chi^2 shows
extremely complicated behavior over the 9-parameter space that characterizes
binary lenses. This makes it difficult to systematically search the space and
verify that a given local minimum is a global minimum. We show that for events
with well-monitored caustics, the caustic-crossing region can be isolated from
the rest of the light curve and easily fit to a 5-parameter function. Four of
these caustic-crossing parameters can then be used to constrain the search in
the larger 9-parameter space. This allows a systematic search for all solutions
and thus identification of all local minima. We illustrate this technique using
the PLANET data for MACHO 98-SMC-1, an excellent and publicly available
caustic-crossing data set. We show that a very broad range of parameter
combinations are compatible with the PLANET data set, demonstrating that
observations of binary-lens lightcurves with sampling of only one caustic
crossing do not yield unique solutions. The corollary to this is that the time
of the second caustic crossing cannot be reliably predicted on the basis of
early data including the first caustic crossing alone. We investigate the
requirements for determination of a unique solution and find that occasional
observations of the first caustic crossing may be sufficient to derive a
complete solution.Comment: 31 pages + 8 figures + 2 table
Combined Analysis of the Binary-Lens Caustic-Crossing Event MACHO 98-SMC-1
We fit the data for the binary-lens microlensing event MACHO 98-SMC-1 from 5
different microlensing collaborations and find two distinct solutions
characterized by binary separation d and mass ratio q: (d,q)=(0.54,0.50) and
(d,q)=(3.65,0.36), where d is in units of the Einstein radius. However, the
relative proper motion of the lens is very similar in the two solutions, 1.30
km/s/kpc and 1.48 km/s/kpc, thus confirming that the lens is in the Small
Magellanic Cloud. The close binary can be either rotating or approximately
static but the wide binary must be rotating at close its maximum allowed rate
to be consistent with all the data. We measure limb-darkening coefficients for
five bands ranging from I to V. As expected, these progressively decrease with
rising wavelength. This is the first measurement of limb darkening for a
metal-poor A star.Comment: 29 pages + 9 figures + 2 tables, submitted to Ap
Recipes for spin-based quantum computing
Technological growth in the electronics industry has historically been
measured by the number of transistors that can be crammed onto a single
microchip. Unfortunately, all good things must come to an end; spectacular
growth in the number of transistors on a chip requires spectacular reduction of
the transistor size. For electrons in semiconductors, the laws of quantum
mechanics take over at the nanometre scale, and the conventional wisdom for
progress (transistor cramming) must be abandoned. This realization has
stimulated extensive research on ways to exploit the spin (in addition to the
orbital) degree of freedom of the electron, giving birth to the field of
spintronics. Perhaps the most ambitious goal of spintronics is to realize
complete control over the quantum mechanical nature of the relevant spins. This
prospect has motivated a race to design and build a spintronic device capable
of complete control over its quantum mechanical state, and ultimately,
performing computations: a quantum computer.
In this tutorial we summarize past and very recent developments which point
the way to spin-based quantum computing in the solid-state. After introducing a
set of basic requirements for any quantum computer proposal, we offer a brief
summary of some of the many theoretical proposals for solid-state quantum
computers. We then focus on the Loss-DiVincenzo proposal for quantum computing
with the spins of electrons confined to quantum dots. There are many obstacles
to building such a quantum device. We address these, and survey recent
theoretical, and then experimental progress in the field. To conclude the
tutorial, we list some as-yet unrealized experiments, which would be crucial
for the development of a quantum-dot quantum computer.Comment: 45 pages, 12 figures (low-res in preprint, high-res in journal)
tutorial review for Nanotechnology; v2: references added and updated, final
version to appear in journa
Projective Hilbert space structures at exceptional points
A non-Hermitian complex symmetric 2x2 matrix toy model is used to study
projective Hilbert space structures in the vicinity of exceptional points
(EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are
Puiseux-expanded in terms of the root vectors at the EP. It is shown that the
apparent contradiction between the two incompatible normalization conditions
with finite and singular behavior in the EP-limit can be resolved by
projectively extending the original Hilbert space. The complementary
normalization conditions correspond then to two different affine charts of this
enlarged projective Hilbert space. Geometric phase and phase jump behavior are
analyzed and the usefulness of the phase rigidity as measure for the distance
to EP configurations is demonstrated. Finally, EP-related aspects of
PT-symmetrically extended Quantum Mechanics are discussed and a conjecture
concerning the quantum brachistochrone problem is formulated.Comment: 20 pages; discussion extended, refs added; bug correcte
Defining the cellular precursors to human breast cancer
Human breast cancers are broadly classified based on their gene-expression profiles into luminal- and basal-type tumors. These two major tumor subtypes express markers corresponding to the major differentiation states of epithelial cells in the breast: luminal (EpCAM+) and basal/myoepithelial (CD10+). However, there are also rare types of breast cancers, such as metaplastic carcinomas, where tumor cells exhibit features of alternate cell types that no longer resemble breast epithelium. Until now, it has been difficult to identify the cell type(s) in the human breast that gives rise to these various forms of breast cancer. Here we report that transformation of EpCAM+ epithelial cells results in the formation of common forms of human breast cancer, including estrogen receptor-positive and estrogen receptor-negative tumors with luminal and basal-like characteristics, respectively, whereas transformation of CD10+ cells results in the development of rare metaplastic tumors reminiscent of the claudin-low subtype. We also demonstrate the existence of CD10+ breast cells with metaplastic traits that can give rise to skin and epidermal tissues. Furthermore, we show that the development of metaplastic breast cancer is attributable, in part, to the transformation of these metaplastic breast epithelial cells. These findings identify normal cellular precursors to human breast cancers and reveal the existence of a population of cells with epidermal progenitor activity within adult human breast tissues
Play Behavior and Attachment in Toddlers with Autism
Play helps to develop social skills. Children with autism show deviances in their play behavior that may be associated with delays in their social development. In this study, we investigated manipulative, functional and symbolic play behavior of toddlers with and without autism (mean age: 26.45, SD 5.63). The results showed that the quality of interaction between the child and the caregiver was related to the development of play behavior. In particular, security of attachment was related to better play behavior. When the developmental level of the child is taken into account, the attachment relationship of the child with the caregiver at this young age is a better predictor of the level of play behavior than the child's disorder
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