1,385 research outputs found
Automatic Spatial Calibration of Ultra-Low-Field MRI for High-Accuracy Hybrid MEG--MRI
With a hybrid MEG--MRI device that uses the same sensors for both modalities,
the co-registration of MRI and MEG data can be replaced by an automatic
calibration step. Based on the highly accurate signal model of ultra-low-field
(ULF) MRI, we introduce a calibration method that eliminates the error sources
of traditional co-registration. The signal model includes complex sensitivity
profiles of the superconducting pickup coils. In ULF MRI, the profiles are
independent of the sample and therefore well-defined. In the most basic form,
the spatial information of the profiles, captured in parallel ULF-MR
acquisitions, is used to find the exact coordinate transformation required. We
assessed our calibration method by simulations assuming a helmet-shaped
pickup-coil-array geometry. Using a carefully constructed objective function
and sufficient approximations, even with low-SNR images, sub-voxel and
sub-millimeter calibration accuracy was achieved. After the calibration,
distortion-free MRI and high spatial accuracy for MEG source localization can
be achieved. For an accurate sensor-array geometry, the co-registration and
associated errors are eliminated, and the positional error can be reduced to a
negligible level.Comment: 11 pages, 8 figures. This work is part of the BREAKBEN project and
has received funding from the European Union's Horizon 2020 research and
innovation programme under grant agreement No 68686
Approach to equilibrium for the phonon Boltzmann equation
We study the asymptotics of solutions of the Boltzmann equation describing
the kinetic limit of a lattice of classical interacting anharmonic oscillators.
We prove that, if the initial condition is a small perturbation of an
equilibrium state, and vanishes at infinity, the dynamics tends diffusively to
equilibrium. The solution is the sum of a local equilibrium state, associated
to conserved quantities that diffuse to zero, and fast variables that are
slaved to the slow ones. This slaving implies the Fourier law, which relates
the induced currents to the gradients of the conserved quantities.Comment: 23 page
Efficient Two-dimensional Subrecoil Raman Cooling of Atoms in a Tripod Configuration
We present an efficient method for subrecoil cooling of neutral atoms by
applying Raman cooling in 2D to a four-level tripod-system. The atoms can be
cooled simultaneously in two directions using only three laser beams. We
describe the cooling process with a simple model showing that the momentum
distribution can be rapidly narrowed to velocity spread down to
, corresponding to effective temperature equal to
. This method opens new possibilities for cooling of neutral
atoms.Comment: 6 pages, 3 figure
Re-entrant melting and freezing in a model system of charged colloids
We studied the phase behavior of charged and sterically stabilized colloids
using confocal microscopy in a less polar solvent (dielectric constant 5.4).
Upon increasing the colloid volume fraction we found a transition from a fluid
to a body centered cubic crystal at 0.0415+/-0.0005, followed by re-entrant
melting at 0.1165+/-0.0015. A second crystal of different symmetry, random
hexagonal close-packed, was formed at a volume fraction around 0.5, similar to
that of hard spheres. We attribute the intriguing phase behavior to particle
interactions that depend strongly on volume fraction, mainly due to changes in
the colloid charge. In this low polarity system the colloids acquire charge
through ion adsorption. The low ionic strength leads to fewer ions per colloid
at elevated volume fractions and consequently a density-dependent colloid
charge.Comment: 25 pages, 5 figures 1 tabl
Tailoring of motional states in double-well potentials by time-dependent processes
We show that the vibrational state tailoring method developed for molecular
systems can be applied for cold atoms in optical lattices. The original method
is based on a three-level model interacting with two strong laser pulses in a
counterintuitive sequence [M. Rodriguez et al., Phys. Rev. A 62, 053413
(2000)]. Here we outline the conditions for achieving similar dynamics with
single time-dependent potential surfaces. It is shown that guided switching
between diabatic and adiabatic evolution has an essential role in this system.
We also show that efficient and precise tailoring of motional states in optical
lattices can be achieved, for instance, simply by superimposing two lattices
and moving them with respect to each other.Comment: 9 pages, 11 figures, 25 references; accepted to PRA; v2: minor
explanatory remarks added & typos correcte
Collective molecule formation in a degenerate Fermi gas via a Feshbach resonance
We model collisionless collective conversion of a degenerate Fermi gas into
bosonic molecules via a Feshbach resonance, treating the bosonic molecules as a
classical field and seeding the pairing amplitudes with random phases. A
dynamical instability of the Fermi sea against association into molecules
initiates the conversion. The model qualitatively reproduces several
experimental observations {[Regal et al., Nature {\bf 424}, 47 (2003)]}. We
predict that the initial temperature of the Fermi gas sets the limit for the
efficiency of atom-molecule conversion.Comment: 4 pages, 3 figures, 10+ references, accepted to PR
Atomic carbon chains as spin-transmitters: an \textit{Ab initio} transport study
An atomic carbon chain joining two graphene flakes was recently realized in a
ground-breaking experiment by Jin {\it et al.}, Phys. Rev. Lett. {\bf 102},
205501 (2009). We present {\it ab initio} results for the electron transport
properties of such chains and demonstrate complete spin-polarization of the
transmission in large energy ranges. The effect is due to the spin-polarized
zig-zag edge terminating each graphene flake causing a spin-splitting of the
graphene bands, and the chain states. Transmission occurs when the
graphene -states resonate with similar states in the strongly hybridized
edges and chain. This effect should in general hold for any -conjugated
molecules bridging the zig-zag edges of graphene electrodes. The polarization
of the transmission can be controlled by chemically or mechanically modifying
the molecule, or by applying an electrical gate
Approach to ground state and time-independent photon bound for massless spin-boson models
It is widely believed that an atom interacting with the electromagnetic field
(with total initial energy well-below the ionization threshold) relaxes to its
ground state while its excess energy is emitted as radiation. Hence, for large
times, the state of the atom+field system should consist of the atom in its
ground state, and a few free photons that travel off to spatial infinity.
Mathematically, this picture is captured by the notion of asymptotic
completeness. Despite some recent progress on the spectral theory of such
systems, a proof of relaxation to the ground state and asymptotic completeness
was/is still missing, except in some special cases (massive photons, small
perturbations of harmonic potentials). In this paper, we partially fill this
gap by proving relaxation to an invariant state in the case where the atom is
modelled by a finite-level system. If the coupling to the field is sufficiently
infrared-regular so that the coupled system admits a ground state, then this
invariant state necessarily corresponds to the ground state. Assuming slightly
more infrared regularity, we show that the number of emitted photons remains
bounded in time. We hope that these results bring a proof of asymptotic
completeness within reach.Comment: 45 pages, published in Annales Henri Poincare. This archived version
differs from the journal version because we corrected an inconsequential
mistake in Section 3.5.1: to do this, a new paragraph was added after Lemma
3.
Knots and Particles
Using methods of high performance computing, we have found indications that
knotlike structures appear as stable finite energy solitons in a realistic 3+1
dimensional model. We have explicitly simulated the unknot and trefoil
configurations, and our results suggest that all torus knots appear as
solitons. Our observations open new theoretical possibilities in scenarios
where stringlike structures appear, including physics of fundamental
interactions and early universe cosmology. In nematic liquid crystals and 3He
superfluids such knotted solitons might actually be observed.Comment: 9 pages, 4 color eps figures and one b/w because of size limit (color
version available from authors
On dimension reduction in Gaussian filters
A priori dimension reduction is a widely adopted technique for reducing the
computational complexity of stationary inverse problems. In this setting, the
solution of an inverse problem is parameterized by a low-dimensional basis that
is often obtained from the truncated Karhunen-Loeve expansion of the prior
distribution. For high-dimensional inverse problems equipped with smoothing
priors, this technique can lead to drastic reductions in parameter dimension
and significant computational savings.
In this paper, we extend the concept of a priori dimension reduction to
non-stationary inverse problems, in which the goal is to sequentially infer the
state of a dynamical system. Our approach proceeds in an offline-online
fashion. We first identify a low-dimensional subspace in the state space before
solving the inverse problem (the offline phase), using either the method of
"snapshots" or regularized covariance estimation. Then this subspace is used to
reduce the computational complexity of various filtering algorithms - including
the Kalman filter, extended Kalman filter, and ensemble Kalman filter - within
a novel subspace-constrained Bayesian prediction-and-update procedure (the
online phase). We demonstrate the performance of our new dimension reduction
approach on various numerical examples. In some test cases, our approach
reduces the dimensionality of the original problem by orders of magnitude and
yields up to two orders of magnitude in computational savings
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