1,757 research outputs found
Transition state theory for wave packet dynamics. II. Thermal decay of Bose-Einstein condensates with long-range interaction
We apply transition state theory to coupled Gaussian wave packets and
calculate thermal decay rates of Bose-Einstein condensates with additional
long-range interaction. The ground state of such a condensate is metastable if
the contact interaction is attractive and a sufficient thermal excitation may
lead to its collapse. The use of transition state theory is made possible by
describing the condensate within a variational framework and locally mapping
the variational parameters to classical phase space as has been demonstrated in
the preceding paper [A. Junginger, J. Main, and G. Wunner, submitted to J.
Phys. A]. We apply this procedure to Gaussian wave packets and present results
for condensates with monopolar 1/r-interaction comparing decay rates obtained
by using different numbers of coupled Gaussian trial wave functions as well as
different normal form orders.Comment: 14 pages, 4 figures, submitted to J. Phys.
Transition state theory for wave packet dynamics. I. Thermal decay in metastable Schr\"odinger systems
We demonstrate the application of transition state theory to wave packet
dynamics in metastable Schr\"odinger systems which are approached by means of a
variational ansatz for the wave function and whose dynamics is described within
the framework of a time-dependent variational principle. The application of
classical transition state theory, which requires knowledge of a classical
Hamilton function, is made possible by mapping the variational parameters to
classical phase space coordinates and constructing an appropriate Hamiltonian
in action variables. This mapping, which is performed by a normal form
expansion of the equations of motion and an additional adaptation to the energy
functional, as well as the requirements to the variational ansatz are discussed
in detail. The applicability of the procedure is demonstrated for a cubic model
potential for which we calculate thermal decay rates of a frozen Gaussian wave
function. The decay rate obtained with a narrow trial wave function agrees
perfectly with the results using the classical normal form of the corresponding
point particle. The results with a broader trial wave function go even beyond
the classical approach, i.e., they agree with those using the quantum normal
form. The method presented here will be applied to Bose-Einstein condensates in
the following paper [A. Junginger, M. Dorwarth, J. Main, and G. Wunner,
submitted to J. Phys. A].Comment: 21 pages, 3 figures, submitted to J. Phys.
Evolutionary Dynamics While Trapped in Resonance: A Keplerian Binary System Perturbed by Gravitational Radiation
The method of averaging is used to investigate the phenomenon of capture into
resonance for a model that describes a Keplerian binary system influenced by
radiation damping and external normally incident periodic gravitational
radiation. The dynamical evolution of the binary orbit while trapped in
resonance is elucidated using the second order partially averaged system. This
method provides a theoretical framework that can be used to explain the main
evolutionary dynamics of a physical system that has been trapped in resonance.Comment: REVTEX Style, Submitte
North Dakota Economic-Demographic Assessment Model (NEDAM): Technical Description
This report describes the logic, structure, data bases, and operational procedures of the North Dakota model.Research Methods/ Statistical Methods,
Breakdown of Conformal Invariance at Strongly Random Critical Points
We consider the breakdown of conformal and scale invariance in random systems
with strongly random critical points. Extending previous results on
one-dimensional systems, we provide an example of a three-dimensional system
which has a strongly random critical point. The average correlation functions
of this system demonstrate a breakdown of conformal invariance, while the
typical correlation functions demonstrate a breakdown of scale invariance. The
breakdown of conformal invariance is due to the vanishing of the correlation
functions at the infinite disorder fixed point, causing the critical
correlation functions to be controlled by a dangerously irrelevant operator
describing the approach to the fixed point. We relate the computation of
average correlation functions to a problem of persistence in the RG flow.Comment: 9 page
Geometrical Models of the Phase Space Structures Governing Reaction Dynamics
Hamiltonian dynamical systems possessing equilibria of stability type display \emph{reaction-type
dynamics} for energies close to the energy of such equilibria; entrance and
exit from certain regions of the phase space is only possible via narrow
\emph{bottlenecks} created by the influence of the equilibrium points. In this
paper we provide a thorough pedagogical description of the phase space
structures that are responsible for controlling transport in these problems. Of
central importance is the existence of a \emph{Normally Hyperbolic Invariant
Manifold (NHIM)}, whose \emph{stable and unstable manifolds} have sufficient
dimensionality to act as separatrices, partitioning energy surfaces into
regions of qualitatively distinct behavior. This NHIM forms the natural
(dynamical) equator of a (spherical) \emph{dividing surface} which locally
divides an energy surface into two components (`reactants' and `products'), one
on either side of the bottleneck. This dividing surface has all the desired
properties sought for in \emph{transition state theory} where reaction rates
are computed from the flux through a dividing surface. In fact, the dividing
surface that we construct is crossed exactly once by reactive trajectories, and
not crossed by nonreactive trajectories, and related to these properties,
minimizes the flux upon variation of the dividing surface.
We discuss three presentations of the energy surface and the phase space
structures contained in it for 2-degree-of-freedom (DoF) systems in the
threedimensional space , and two schematic models which capture many of
the essential features of the dynamics for -DoF systems. In addition, we
elucidate the structure of the NHIM.Comment: 44 pages, 38 figures, PDFLaTe
Role of heavy-meson exchange in pion production near threshold
Recent calculations of -wave pion production have severely underestimated
the accurately known \ total cross section near
threshold. In these calculations, only the single-nucleon axial-charge operator
is considered. We have calculated, in addition to the one-body term, the
two-body contributions to this reaction that arise from the exchange of mesons.
We find that the inclusion of the scalar -meson exchange current (and
lesser contributions from other mesons) increases the cross section by about a
factor of five, and leads to excellent agreement with the data. The results are
neither very sensitive to changes in the distorting potential that generates
the wave function, nor to different choices for the meson-nucleon form
factors. We argue that \ data provide direct
experimental evidence for meson-exchange contributions to the axial current.Comment: 28 Pages, IU-NTC #93-0
Detectors and cryostat design for the SuMIRe Prime Focus Spectrograph (PFS)
We describe the conceptual design of the camera cryostats, detectors, and
detector readout electronics for the SuMIRe Prime Focus Spectrograph (PFS)
being developed for the Subaru telescope. The SuMIRe PFS will consist of four
identical spectrographs, each receiving 600 fibers from a 2400 fiber robotic
positioner at the prime focus. Each spectrograph will have three channels
covering wavelength ranges 3800 {\AA} - 6700 {\AA}, 6500 {\AA} - 10000 {\AA},
and 9700 {\AA} - 13000 {\AA}, with the dispersed light being imaged in each
channel by a f/1.10 vacuum Schmidt camera. In the blue and red channels a pair
of Hamamatsu 2K x 4K edge-buttable CCDs with 15 um pixels are used to form a 4K
x 4K array. For the IR channel, the new Teledyne 4K x 4K, 15 um pixel,
mercury-cadmium-telluride sensor with substrate removed for short-wavelength
response and a 1.7 um cutoff will be used. Identical detector geometry and a
nearly identical optical design allow for a common cryostat design with the
only notable difference being the need for a cold radiation shield in the IR
camera to mitigate thermal background. This paper describes the details of the
cryostat design and cooling scheme, relevant thermal considerations and
analysis, and discusses the detectors and detector readout electronics
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