14,899 research outputs found
Scattering Theory for Quantum Hall Anyons in a Saddle Point Potential
We study the theory of scattering of two anyons in the presence of a
quadratic saddle-point potential and a perpendicular magnetic field. The
scattering problem decouples in the centre-of-mass and the relative
coordinates. The scattering theory for the relative coordinate encodes the
effects of anyon statistics in the two-particle scattering. This is fully
characterized by two energy-dependent scattering phase shifts. We develop a
method to solve this scattering problem numerically, using a generalized lowest
Landau level approximation.Comment: 5 pages. Published version, with clarified presentatio
Gaussian systems for quantum enhanced multiple phase estimation
For a fixed average energy, the simultaneous estimation of multiple phases
can provide a better total precision than estimating them individually. We show
this for a multimode interferometer with a phase in each mode, using Gaussian
inputs and passive elements, by calculating the covariance matrix. The quantum
Cram\'{e}r-Rao bound provides a lower bound to the covariance matrix via the
quantum Fisher information matrix, whose elements we derive to be the
covariances of the photon numbers across the modes. We prove that this bound
can be saturated. In spite of the Gaussian nature of the problem, the
calculation of non-Gaussian integrals is required, which we accomplish
analytically. We find our simultaneous strategy to yield no more than a
factor-of-2 improvement in total precision, possibly because of a fundamental
performance limitation of Gaussian states. Our work shows that no modal
entanglement is necessary for simultaneous quantum-enhanced estimation of
multiple phases
Spectroscopic properties of large open quantum-chaotic cavities with and without separated time scales
The spectroscopic properties of an open large Bunimovich cavity are studied
numerically in the framework of the effective Hamiltonian formalism. The cavity
is opened by attaching leads to it in four different ways. In some cases,
short-lived and long-lived resonance states coexist. The short-lived states
cause traveling waves in the transmission while the long-lived ones generate
superposed fluctuations. The traveling waves oscillate as a function of energy.
They are not localized in the interior of the large chaotic cavity. In other
cases, the transmission takes place via standing waves with an intensity that
closely follows the profile of the resonances. In all considered cases, the
phase rigidity fluctuates with energy. It is mostly near to its maximum value
and agrees well with the theoretical value for the two-channel case. As shown
in the foregoing paper \cite{1}, all cases are described well by the Poisson
kernel when the calculation is restricted to an energy region in which the
average matrix is (nearly) constant.Comment: 13 pages, 4 figure
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Linking maternity data for England 2007: methods and data quality
Maternity Hospital Episode Statistics (HES) data for 2007 were linked to birth registration and NHS Numbers for Babies (NN4B) data to bring together some key demographic and clinical data items not otherwise available at a national level. This extended the time period 2005-06, for which data had previously been linked and reported
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Birth outcomes for African and Caribbean babies in England and Wales: retrospective analysis of routinely collected data
Objectives: To compare mean birth weights, gestational ages and odds of preterm birth and low birth weight of live singleton babies of black African or Caribbean ethnicity born in 2005 or 2006 by mother's country of birth.
Design: Secondary analysis of data from linked birth registration and NHS Numbers for Babies data set.
Setting: Births to women in England and Wales in 2005 and 2006.
Participants: Babies of African and Caribbean ethnicity born in England and Wales in 2005â2006, whose mothers were born in African and Caribbean countries or the UK. Birth outcomes for 51 599 singleton births were analysed.
Main outcome measures: Gestational age and birth weight.
Results: Mothers born in Eastern or Northern Africa had babies at higher mean gestational ages (39.38 and 39.41 weeks, respectively) and lower odds of preterm birth (OR=0.80 and 0.65, respectively) compared with 39.00 weeks for babies with mothers born in the UK. Babies of African ethnicity whose mothers were born in Middle or Western Africa had mean birth weights of 3327 and 3311 g, respectively. These were significantly higher than the mean birth weight of 3257 g for babies of the UK-born mothers. Their odds of low birth weight (OR=0.75 and 0.72, respectively) were significantly lower. Babies of Caribbean ethnicity whose mothers were born in the Caribbean had higher mean birth weight and lower odds of low birth weight than those whose mothers were born in the UK.
Conclusions: The study shows that in babies of African and Caribbean ethnicity, rates of low birth weight and preterm birth varied by mothers' countries of birth. Ethnicity and country of birth are important factors associated with perinatal health, but assessing them singly can mask important heterogeneity in birth outcomes within categories particularly in relation to African ethnicity. These differences should be explored further
Space Complexity of Perfect Matching in Bounded Genus Bipartite Graphs
We investigate the space complexity of certain perfect matching problems over
bipartite graphs embedded on surfaces of constant genus (orientable or
non-orientable). We show that the problems of deciding whether such graphs have
(1) a perfect matching or not and (2) a unique perfect matching or not, are in
the logspace complexity class \SPL. Since \SPL\ is contained in the logspace
counting classes \oplus\L (in fact in \modk\ for all ), \CeqL, and
\PL, our upper bound places the above-mentioned matching problems in these
counting classes as well. We also show that the search version, computing a
perfect matching, for this class of graphs is in \FL^{\SPL}. Our results
extend the same upper bounds for these problems over bipartite planar graphs
known earlier. As our main technical result, we design a logspace computable
and polynomially bounded weight function which isolates a minimum weight
perfect matching in bipartite graphs embedded on surfaces of constant genus. We
use results from algebraic topology for proving the correctness of the weight
function.Comment: 23 pages, 13 figure
Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime
We study the transmission through different small systems as a function of
the coupling strength to the two attached leads. The leads are identical
with only one propagating mode in each of them. Besides the
conductance , we calculate the phase rigidity of the scattering wave
function in the interior of the system. Most interesting results are
obtained in the regime of strongly overlapping resonance states where the
crossover from staying to traveling modes takes place. The crossover is
characterized by collective effects. Here, the conductance is plateau-like
enhanced in some energy regions of finite length while corridors with zero
transmission (total reflection) appear in other energy regions. This
transmission picture depends only weakly on the spectrum of the closed system.
It is caused by the alignment of some resonance states of the system with the
propagating modes in the leads. The alignment of resonance states
takes place stepwise by resonance trapping, i.e. it is accompanied by the
decoupling of other resonance states from the continuum of propagating modes.
This process is quantitatively described by the phase rigidity of the
scattering wave function. Averaged over energy in the considered energy window,
is correlated with . In the regime of strong coupling, only two
short-lived resonance states survive each aligned with one of the channel wave
functions . They may be identified with traveling modes through the
system. The remaining trapped narrow resonance states are well separated
from one another.Comment: Resonance trapping mechanism explained in the captions of Figs. 7 to
11. Recent papers added in the list of reference
Partial Isometries of a Sub-Riemannian Manifold
In this paper, we obtain the following generalisation of isometric
-immersion theorem of Nash and Kuiper. Let be a smooth manifold of
dimension and a rank subbundle of the tangent bundle with a
Riemannian metric . Then the pair defines a sub-Riemannian
structure on . We call a -map into a Riemannian
manifold a {\em partial isometry} if the derivative map restricted
to is isometric; in other words, . The main result states that
if then a smooth -immersion satisfying
can be homotoped to a partial isometry which is
-close to . In particular we prove that every sub-Riemannian manifold
admits a partial isometry in provided .Comment: 13 pages. This is a revised version of an earlier submission (minor
revision
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