2,300 research outputs found
Ground state cooling of atoms in optical lattices
We propose two schemes for cooling bosonic and fermionic atoms that are
trapped in a deep optical lattice. The first scheme is a quantum algorithm
based on particle number filtering and state dependent lattice shifts. The
second protocol alternates filtering with a redistribution of particles by
means of quantum tunnelling. We provide a complete theoretical analysis of both
schemes and characterize the cooling efficiency in terms of the entropy. Our
schemes do not require addressing of single lattice sites and use a novel
method, which is based on coherent laser control, to perform very fast
filtering.Comment: 12 pages, 7 figure
The Power of Light Zine 1 - Why do things change? - an epistemically insightful way to explore the nature of science and research at Diamond Light Source, UK
In the STFC funded Epistemic Insight Initiative project, The Power of Light, a series of resources have been designed informed by co-creation activities, pilot lessons, and workshops that involved children in schools and with their families in community spaces. Through this project with Diamond, we brought into classrooms and community spaces how light can be used to help investigate the world around us, address real-world problems and inform our thinking about Big Questions. The resources we develop support teachers' and their students' sense of agency when exploring 'how knowledge works' and how knowledge is built through different disciplines (including the natural sciences, the arts, and the humanities).
This 'zine', with its focus on how scientists have been working with historians and archaeologists to preserve the Mary Rose (Henry the Eighth's favourite ship that was sunk in the Solent in England's southern coast), has been developed through co-creative activities involving research scientists at Diamond Light Source (UK), academics, primary school teachers, STEM ambassadors, and Diamond's public engagement team.
Zines use an appealing combination of text and images to create a concise comic-like narrative format to generate enthusiasm about a particular area of interest - the series of zines designed for this project focuses on research taking place at the Diamond facility. The Diamond Light Source facility houses a synchrotron which is used to conduct research in a variety of applied fields of science and technology.
This zine is designed to be accessible to ages 8+, and works well with a short animation (available in both Zenodo and on the Epistemic Insight You Tube channel) that has been created with additional funding from STFC. Teaching notes are available for this zine, with guidance and activity sheets to support working with the Power of Light resources.
This zine explores these discussion questions: 1) What are examples of changes we can observe? 2) What helps us to know more about the things around us? 3) What might we use to help us observe changes
Maximum likelihood drift estimation for a threshold diffusion
We study the maximum likelihood estimator of the drift parameters of a
stochastic differential equation, with both drift and diffusion coefficients
constant on the positive and negative axis, yet discontinuous at zero. This
threshold diffusion is called drifted Oscillating Brownian motion.For this
continuously observed diffusion, the maximum likelihood estimator coincide with
a quasi-likelihood estimator with constant diffusion term. We show that this
estimator is the limit, as observations become dense in time, of the
(quasi)-maximum likelihood estimator based on discrete observations. In long
time, the asymptotic behaviors of the positive and negative occupation times
rule the ones of the estimators. Differently from most known results in the
literature, we do not restrict ourselves to the ergodic framework: indeed,
depending on the signs of the drift, the process may be ergodic, transient or
null recurrent. For each regime, we establish whether or not the estimators are
consistent; if they are, we prove the convergence in long time of the properly
rescaled difference of the estimators towards a normal or mixed normal
distribution. These theoretical results are backed by numerical simulations
A general central limit theorem and a subsampling variance estimator for α‐mixing point processes
Information Loss in Coarse Graining of Polymer Configurations via Contact Matrices
Contact matrices provide a coarse grained description of the configuration
omega of a linear chain (polymer or random walk) on Z^n: C_{ij}(omega)=1 when
the distance between the position of the i-th and j-th step are less than or
equal to some distance "a" and C_{ij}(omega)=0 otherwise. We consider models in
which polymers of length N have weights corresponding to simple and
self-avoiding random walks, SRW and SAW, with "a" the minimal permissible
distance. We prove that to leading order in N, the number of matrices equals
the number of walks for SRW, but not for SAW. The coarse grained Shannon
entropies for SRW agree with the fine grained ones for n <= 2, but differs for
n >= 3.Comment: 18 pages, 2 figures, latex2e Main change: the introduction is
rewritten in a less formal way with the main results explained in simple
term
A Holder Continuous Nowhere Improvable Function with Derivative Singular Distribution
We present a class of functions in which is variant
of the Knopp class of nowhere differentiable functions. We derive estimates
which establish \mathcal{K} \sub C^{0,\al}(\R) for 0<\al<1 but no is pointwise anywhere improvable to C^{0,\be} for any \be>\al.
In particular, all 's are nowhere differentiable with derivatives singular
distributions. furnishes explicit realizations of the functional
analytic result of Berezhnoi.
Recently, the author and simulteously others laid the foundations of
Vector-Valued Calculus of Variations in (Katzourakis), of
-Extremal Quasiconformal maps (Capogna and Raich, Katzourakis) and of
Optimal Lipschitz Extensions of maps (Sheffield and Smart). The "Euler-Lagrange
PDE" of Calculus of Variations in is the nonlinear nondivergence
form Aronsson PDE with as special case the -Laplacian.
Using , we construct singular solutions for these PDEs. In the
scalar case, we partially answered the open regularity problem of
Viscosity Solutions to Aronsson's PDE (Katzourakis). In the vector case, the
solutions can not be rigorously interpreted by existing PDE theories and
justify our new theory of Contact solutions for fully nonlinear systems
(Katzourakis). Validity of arguments of our new theory and failure of classical
approaches both rely on the properties of .Comment: 5 figures, accepted to SeMA Journal (2012), to appea
Level Sets of the Takagi Function: Local Level Sets
The Takagi function \tau : [0, 1] \to [0, 1] is a continuous
non-differentiable function constructed by Takagi in 1903. The level sets L(y)
= {x : \tau(x) = y} of the Takagi function \tau(x) are studied by introducing a
notion of local level set into which level sets are partitioned. Local level
sets are simple to analyze, reducing questions to understanding the relation of
level sets to local level sets, which is more complicated. It is known that for
a "generic" full Lebesgue measure set of ordinates y, the level sets are finite
sets. Here it is shown for a "generic" full Lebesgue measure set of abscissas
x, the level set L(\tau(x)) is uncountable. An interesting singular monotone
function is constructed, associated to local level sets, and is used to show
the expected number of local level sets at a random level y is exactly 3/2.Comment: 32 pages, 2 figures, 1 table. Latest version has updated equation
numbering. The final publication will soon be available at springerlink.co
Search for gravitational waves associated with the August 2006 timing glitch of the Vela pulsar
The physical mechanisms responsible for pulsar timing glitches are thought to excite quasinormal mode oscillations in their parent neutron star that couple to gravitational-wave emission. In August 2006, a timing glitch was observed in the radio emission of PSR B0833-45, the Vela pulsar. At the time of the glitch, the two colocated Hanford gravitational-wave detectors of the Laser Interferometer Gravitational wave observatory (LIGO) were operational and taking data as part of the fifth LIGO science run (S5). We present the first direct search for the gravitational-wave emission associated with oscillations of the fundamental quadrupole mode excited by a pulsar timing glitch. No gravitational-wave detection
candidate was found. We place Bayesian 90% confidence upper limits of 6.3 x 10^(-21) to 1.4 x 10^(-20) on the peak intrinsic strain amplitude of gravitational-wave ring-down signals, depending on which spherical harmonic mode is excited. The corresponding range of energy upper limits is 5.0 x 10^(-44) to 1.3 x 10^(-45) erg
Self-similar stable processes arising from high-density limits of occupation times of particle systems
We extend results on time-rescaled occupation time fluctuation limits of the
-branching particle system with Poisson initial condition. The earlier results in the homogeneous case
(i.e., with Lebesgue initial intensity measure) were obtained for dimensions
only, since the particle system becomes locally extinct if
. In this paper we show that by introducing high density
of the initial Poisson configuration, limits are obtained for all dimensions,
and they coincide with the previous ones if . We also give
high-density limits for the systems with finite intensity measures (without
high density no limits exist in this case due to extinction); the results are
different and harder to obtain due to the non-invariance of the measure for the
particle motion. In both cases, i.e., Lebesgue and finite intensity measures,
for low dimensions ( and
, respectively) the limits are determined by
non-L\'evy self-similar stable processes. For the corresponding high dimensions
the limits are qualitatively different: -valued L\'evy
processes in the Lebesgue case, stable processes constant in time on
in the finite measure case. For high dimensions, the laws of all
limit processes are expressed in terms of Riesz potentials. If , the
limits are Gaussian. Limits are also given for particle systems without
branching, which yields in particular weighted fractional Brownian motions in
low dimensions. The results are obtained in the setup of weak convergence of
S'(R^d)$-valued processes.Comment: 28 page
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