13,535 research outputs found
A variational problem on Stiefel manifolds
In their paper on discrete analogues of some classical systems such as the
rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced
their analysis in the general context of flows on Stiefel manifolds. We
consider here a general class of continuous time, quadratic cost, optimal
control problems on Stiefel manifolds, which in the extreme dimensions again
yield these classical physical geodesic flows. We have already shown that this
optimal control setting gives a new symmetric representation of the rigid body
flow and in this paper we extend this representation to the geodesic flow on
the ellipsoid and the more general Stiefel manifold case. The metric we choose
on the Stiefel manifolds is the same as that used in the symmetric
representation of the rigid body flow and that used by Moser and Veselov. In
the extreme cases of the ellipsoid and the rigid body, the geodesic flows are
known to be integrable. We obtain the extremal flows using both variational and
optimal control approaches and elucidate the structure of the flows on general
Stiefel manifolds.Comment: 30 page
Discrimination of the Healthy and Sick Cardiac Autonomic Nervous System by a New Wavelet Analysis of Heartbeat Intervals
We demonstrate that it is possible to distinguish with a complete certainty
between healthy subjects and patients with various dysfunctions of the cardiac
nervous system by way of multiresolutional wavelet transform of RR intervals.
We repeated the study of Thurner et al on different ensemble of subjects. We
show that reconstructed series using a filter which discards wavelet
coefficients related with higher scales enables one to classify individuals for
which the method otherwise is inconclusive. We suggest a delimiting diagnostic
value of the standard deviation of the filtered, reconstructed RR interval time
series in the range of (for the above mentioned filter), below
which individuals are at risk.Comment: 5 latex pages (including 6 figures). Accepted in Fractal
Experimental realization of plaquette resonating valence bond states with ultracold atoms in optical superlattices
The concept of valence bond resonance plays a fundamental role in the theory
of the chemical bond and is believed to lie at the heart of many-body quantum
physical phenomena. Here we show direct experimental evidence of a
time-resolved valence bond quantum resonance with ultracold bosonic atoms in an
optical lattice. By means of a superlattice structure we create a
three-dimensional array of independent four-site plaquettes, which we can fully
control and manipulate in parallel. Moreover, we show how small-scale plaquette
resonating valence bond states with s- and d-wave symmetry can be created and
characterized. We anticipate our findings to open the path towards the creation
and analysis of many-body RVB states in ultracold atomic gases.Comment: 7 page, 4 figures in main text, 3 figures in appendi
Controllable diffusion of cold atoms in a harmonically driven and tilted optical lattice: Decoherence by spontaneous emission
We have studied some transport properties of cold atoms in an accelerated
optical lattice in the presence of decohering effects due to spontaneous
emission. One new feature added is the effect of an external AC drive. As a
result we obtain a tunable diffusion coefficient and it's nonlinear enhancement
with increasing drive amplitude. We report an interesting maximum diffusion
condition.Comment: 16 pages, 7 figures, revised versio
Imaging a single atom in a time-of-flight experiment
We perform fluorescence imaging of a single 87Rb atom after its release from
an optical dipole trap. The time-of-flight expansion of the atomic spatial
density distribution is observed by accumulating many single atom images. The
position of the atom is revealed with a spatial resolution close to 1
micrometer by a single photon event, induced by a short resonant probe. The
expansion yields a measure of the temperature of a single atom, which is in
very good agreement with the value obtained by an independent measurement based
on a release-and-recapture method. The analysis presented in this paper
provides a way of calibrating an imaging system useful for experimental studies
involving a few atoms confined in a dipole trap.Comment: 14 pages, 8 figure
The Molecular Clockwork of the Fire Ant Solenopsis invicta
This is an open-access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication
Pricing in Social Networks with Negative Externalities
We study the problems of pricing an indivisible product to consumers who are
embedded in a given social network. The goal is to maximize the revenue of the
seller. We assume impatient consumers who buy the product as soon as the seller
posts a price not greater than their values of the product. The product's value
for a consumer is determined by two factors: a fixed consumer-specified
intrinsic value and a variable externality that is exerted from the consumer's
neighbors in a linear way. We study the scenario of negative externalities,
which captures many interesting situations, but is much less understood in
comparison with its positive externality counterpart. We assume complete
information about the network, consumers' intrinsic values, and the negative
externalities. The maximum revenue is in general achieved by iterative pricing,
which offers impatient consumers a sequence of prices over time.
We prove that it is NP-hard to find an optimal iterative pricing, even for
unweighted tree networks with uniform intrinsic values. Complementary to the
hardness result, we design a 2-approximation algorithm for finding iterative
pricing in general weighted networks with (possibly) nonuniform intrinsic
values. We show that, as an approximation to optimal iterative pricing, single
pricing can work rather well for many interesting cases, but theoretically it
can behave arbitrarily bad
Landau-Zener sweeps and sudden quenches in coupled Bose-Hubbard chains
We simulate numerically the dynamics of strongly correlated bosons in a
two-leg ladder subject to a time-dependent energy bias between the two chains.
When all atoms are initially in the leg with higher energy, we find a drastic
reduction of the inter-chain particle transfer for slow linear sweeps, in
quantitative agreement with recent experiments. This effect is preceded by a
rapid broadening of the quasi-momentum distribution of atoms, signaling the
presence of a bath of low-energy excitations in the chains. We further
investigate the scenario of quantum quenches to fixed values of the energy
bias. We find that for large enough density the momentum distribution relaxes
to that of an equilibrium thermal state with the same energy.Comment: 6 pages, 4 figure
Pseudogap in fermionic density of states in the BCS-BEC crossover of atomic Fermi gases
We study pseudogap behaviors of ultracold Fermi gases in the BCS-BEC
crossover region. We calculate the density of states (DOS), as well as the
single-particle spectral weight, above the superfluid transition temperature
including pairing fluctuations within a -matrix approximation.
We find that DOS exhibits a pseudogap structure in the BCS-BEC crossover
region, which is most remarkable near the unitarity limit. We determine the
pseudogap temperature at which the pseudogap structure in DOS disappears.
We also introduce another temperature at which the BCS-like
double-peak structure disappears in the spectral weight. While one finds
in the BCS regime, becomes higher than in the
crossover and BEC regime. We also determine the pseudogap region in the phase
diagram in terms of temperature and pairing interaction.Comment: 6 pages, 4 figures, Proceedings of QFS 200
- …