5,867 research outputs found
Stable Quantum Resonances in Atom Optics
A theory for stabilization of quantum resonances by a mechanism similar to
one leading to classical resonances in nonlinear systems is presented. It
explains recent surprising experimental results, obtained for cold Cesium atoms
when driven in the presence of gravity, and leads to further predictions. The
theory makes use of invariance properties of the system, that are similar to
those of solids, allowing for separation into independent kicked rotor
problems. The analysis relies on a fictitious classical limit where the small
parameter is {\em not} Planck's constant, but rather the detuning from the
frequency that is resonant in absence of gravity.Comment: 5 pages, 3 figure
The Ulysses Supplement to the BATSE 4Br Catalog of Cosmic Gamma-Ray Bursts
We present Interplanetary Network localization information for 147 gamma-ray
bursts observed by the Burst and Transient Source Experiment between the end of
the 3rd BATSE catalog and the end of the 4th BATSE catalog, obtained by
analyzing the arrival times of these bursts at the Ulysses and Compton
Gamma-Ray Observatory (CGRO) spacecraft. For any given burst observed by these
two spacecraft, arrival time analysis (or "triangulation") results in an
annulus of possible arrival directions whose half-width varies between 7
arcseconds and 2.3 degrees, depending on the intensity and time history of the
burst, and the distance of the Ulysses spacecraft from Earth. This annulus
generally intersects the BATSE error circle, resulting in an average reduction
of the error box area of a factor of 25.Comment: Accepted for publication in the Astrophysical Journal Supplemen
Likelihood Analysis of Repeating in the BATSE Catalogue
I describe a new likelihood technique, based on counts-in-cells statistics,
that I use to analyze repeating in the BATSE 1B and 2B catalogues. Using the 1B
data, I find that repeating is preferred over non-repeating by 4.3:1 odds, with
a well-defined peak at 5-6 repetitions per source. I find that the post-1B data
are consistent with the repeating model inferred from the 1B data, after taking
into account the lower fraction of bursts with well-determined positions.
Combining the two data sets, I find that the odds favoring repeating over
non-repeating are almost unaffected at 4:1, with a narrower peak at 5
repetitions per source. I conclude that the data sets are consistent both with
each other and with repeating, and that for these data sets the odds favor
repeating.Comment: 5 pages including 3 encapsulated figures, as a uuencoded, gzipped,
Postscript file. To appear in Proc. of the 1995 La Jolla workshop ``High
Velocity Neutron Stars and Gamma-Ray Bursts'' eds. Rothschild, R. et al.,
AIP, New Yor
Echoes and revival echoes in systems of anharmonically confined atoms
We study echoes and what we call 'revival echoes' for a collection of atoms
that are described by a single quantum wavefunction and are confined in a
weakly anharmonic trap. The echoes and revival echoes are induced by applying
two, successive temporally localized potential perturbations to the confining
potential, one at time , and a smaller one at time . Pulse-like
responses in the expectation value of position are predicted at $t
\approx n\tau$ ($n=2,3,...$) and are particularly evident at $t \approx 2\tau$.
A novel result of our study is the finding of 'revival echoes'. Revivals (but
not echoes) occur even if the second perturbation is absent. In particular, in
the absence of the second perturbation, the response to the first perturbation
dies away, but then reassembles, producing a response at revival times $mT_x$
($m=1,2,...$). Including the second perturbation at $t=\tau$, we find
temporally localized responses, revival echoes, both before and after $t\approx
mT_x$, e.g., at $t\approx m T_x-n \tau$ (pre-revival echoes) and at $t\approx
mT_x+n\tau$, (post-revival echoes), where $m$ and $n$ are $1,2,...$ . Depending
on the form of the perturbations, the 'principal' revival echoes at $t \approx
T_x \pm \tau$ can be much larger than the echo at $t \approx 2\tau$. We develop
a perturbative model for these phenomena, and compare its predictions to the
numerical solutions of the time-dependent Schr\"odinger Equation. The scaling
of the size of the various echoes and revival echoes as a function of the
symmetry and size of the perturbations applied at $t=0$ and $t=\tau$ is
investigated. We also study the presence of revivals and revival echoes in
higher moments of position, , , and the effect of atom-atom
interactions on these phenomena.Comment: 33 pages, 13 figures, corrected typos and added reference
Scaling and Universality of the Complexity of Analog Computation
We apply a probabilistic approach to study the computational complexity of
analog computers which solve linear programming problems. We analyze
numerically various ensembles of linear programming problems and obtain, for
each of these ensembles, the probability distribution functions of certain
quantities which measure the computational complexity, known as the convergence
rate, the barrier and the computation time. We find that in the limit of very
large problems these probability distributions are universal scaling functions.
In other words, the probability distribution function for each of these three
quantities becomes, in the limit of large problem size, a function of a single
scaling variable, which is a certain composition of the quantity in question
and the size of the system. Moreover, various ensembles studied seem to lead
essentially to the same scaling functions, which depend only on the variance of
the ensemble. These results extend analytical and numerical results obtained
recently for the Gaussian ensemble, and support the conjecture that these
scaling functions are universal.Comment: 22 pages, latex, 12 eps fig
A numerical and symbolical approximation of the Nonlinear Anderson Model
A modified perturbation theory in the strength of the nonlinear term is used
to solve the Nonlinear Schroedinger Equation with a random potential. It is
demonstrated that in some cases it is more efficient than other methods.
Moreover we obtain error estimates. This approach can be useful for the
solution of other nonlinear differential equations of physical relevance.Comment: 21 pages and 7 figure
Chaotic systems in complex phase space
This paper examines numerically the complex classical trajectories of the
kicked rotor and the double pendulum. Both of these systems exhibit a
transition to chaos, and this feature is studied in complex phase space.
Additionally, it is shown that the short-time and long-time behaviors of these
two PT-symmetric dynamical models in complex phase space exhibit strong
qualitative similarities.Comment: 22 page, 16 figure
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