37,100 research outputs found
Condensate splitting in an asymmetric double well for atom chip based sensors
We report on the adiabatic splitting of a BEC of Rb atoms by an
asymmetric double-well potential located above the edge of a perpendicularly
magnetized TbGdFeCo film atom chip. By controlling the barrier height and
double-well asymmetry the sensitivity of the axial splitting process is
investigated through observation of the fractional atom distribution between
the left and right wells. This process constitutes a novel sensor for which we
infer a single shot sensitivity to gravity fields of . From a simple analytic model we propose improvements
to chip-based gravity detectors using this demonstrated methodology.Comment: 4 pages, 5 figure
Coherent states and the quantization of 1+1-dimensional Yang-Mills theory
This paper discusses the canonical quantization of 1+1-dimensional Yang-Mills
theory on a spacetime cylinder, from the point of view of coherent states, or
equivalently, the Segal-Bargmann transform. Before gauge symmetry is imposed,
the coherent states are simply ordinary coherent states labeled by points in an
infinite-dimensional linear phase space. Gauge symmetry is imposed by
projecting the original coherent states onto the gauge-invariant subspace,
using a suitable regularization procedure. We obtain in this way a new family
of "reduced" coherent states labeled by points in the reduced phase space,
which in this case is simply the cotangent bundle of the structure group K.
The main result explained here, obtained originally in a joint work of the
author with B. Driver, is this: The reduced coherent states are precisely those
associated to the generalized Segal-Bargmann transform for K, as introduced by
the author from a different point of view. This result agrees with that of K.
Wren, who uses a different method of implementing the gauge symmetry. The
coherent states also provide a rigorous way of making sense out of the quantum
Hamiltonian for the unreduced system.
Various related issues are discussed, including the complex structure on the
reduced phase space and the question of whether quantization commutes with
reduction
Asymptotic iteration method for eigenvalue problems
An asymptotic interation method for solving second-order homogeneous linear
differential equations of the form y'' = lambda(x) y' + s(x) y is introduced,
where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to
Schroedinger type problems, including some with highly singular potentials, are
presented.Comment: 14 page
Aerodynamics of lift fan V/STOL aircraft
Aerodynamic characteristics of lift fan installation for direct lift V/STOL aircraf
A Bohmian approach to quantum fractals
A quantum fractal is a wavefunction with a real and an imaginary part
continuous everywhere, but differentiable nowhere. This lack of
differentiability has been used as an argument to deny the general validity of
Bohmian mechanics (and other trajectory--based approaches) in providing a
complete interpretation of quantum mechanics. Here, this assertion is overcome
by means of a formal extension of Bohmian mechanics based on a limiting
approach. Within this novel formulation, the particle dynamics is always
satisfactorily described by a well defined equation of motion. In particular,
in the case of guidance under quantum fractals, the corresponding trajectories
will also be fractal.Comment: 19 pages, 3 figures (revised version
Effect of Magnetization Inhomogeneity on Magnetic Microtraps for Atoms
We report on the origin of fragmentation of ultracold atoms observed on a
permanent magnetic film atom chip. A novel technique is used to characterize
small spatial variations of the magnetic field near the film surface using
radio frequency spectroscopy of the trapped atoms. Direct observations indicate
the fragmentation is due to a corrugation of the magnetic potential caused by
long range inhomogeneity in the film magnetization. A model which takes into
account two-dimensional variations of the film magnetization is consistent with
the observations.Comment: 4 pages, 4 figure
The Nonexistence of Instrumental Variables
The method of instrumental variables (IV) and the generalized method of moments (GMM) has become a central technique in health economics as a method to help to disentangle the complex question of causality. However the application of these techniques require data on a sufficient number of instrumental variables which are both independent and relevant. We argue that in general such instruments cannot exist. This is a reason for the widespread finding of weak instruments.
Precision measurements of s-wave scattering lengths in a two-component Bose-Einstein condensate
We use collective oscillations of a two-component Bose-Einstein condensate
(2CBEC) of \Rb atoms prepared in the internal states and for the precision measurement of
the interspecies scattering length with a relative uncertainty of
. We show that in a cigar-shaped trap the three-dimensional
(3D) dynamics of a component with a small relative population can be
conveniently described by a one-dimensional (1D) Schr\"{o}dinger equation for
an effective harmonic oscillator. The frequency of the collective oscillations
is defined by the axial trap frequency and the ratio , where
is the intra-species scattering length of a highly populated component
1, and is largely decoupled from the scattering length , the total atom
number and loss terms. By fitting numerical simulations of the coupled
Gross-Pitaevskii equations to the recorded temporal evolution of the axial
width we obtain the value , where is the Bohr
radius. Our reported value is in a reasonable agreement with the theoretical
prediction but deviates significantly from the
previously measured value \cite{Mertes07} which is commonly
used in the characterisation of spin dynamics in degenerate \Rb atoms. Using
Ramsey interferometry of the 2CBEC we measure the scattering length
which also deviates from the previously reported value
\cite{Mertes07}. We characterise two-body losses for the
component 2 and obtain the loss coefficients
and
.Comment: 11 pages, 8 figure
Coherent states on spheres
We describe a family of coherent states and an associated resolution of the
identity for a quantum particle whose classical configuration space is the
d-dimensional sphere S^d. The coherent states are labeled by points in the
associated phase space T*(S^d). These coherent states are NOT of Perelomov type
but rather are constructed as the eigenvectors of suitably defined annihilation
operators. We describe as well the Segal-Bargmann representation for the
system, the associated unitary Segal-Bargmann transform, and a natural
inversion formula. Although many of these results are in principle special
cases of the results of B. Hall and M. Stenzel, we give here a substantially
different description based on ideas of T. Thiemann and of K. Kowalski and J.
Rembielinski. All of these results can be generalized to a system whose
configuration space is an arbitrary compact symmetric space. We focus on the
sphere case in order to be able to carry out the calculations in a
self-contained and explicit way.Comment: Revised version. Submitted to J. Mathematical Physic
- …