16,297 research outputs found
On the Use of Group Theoretical and Graphical Techniques toward the Solution of the General N-body Problem
Group theoretic and graphical techniques are used to derive the N-body wave
function for a system of identical bosons with general interactions through
first-order in a perturbation approach. This method is based on the maximal
symmetry present at lowest order in a perturbation series in inverse spatial
dimensions. The symmetric structure at lowest order has a point group
isomorphic with the S_N group, the symmetric group of N particles, and the
resulting perturbation expansion of the Hamiltonian is order-by-order invariant
under the permutations of the S_N group. This invariance under S_N imposes
severe symmetry requirements on the tensor blocks needed at each order in the
perturbation series. We show here that these blocks can be decomposed into a
basis of binary tensors invariant under S_N. This basis is small (25 terms at
first order in the wave function), independent of N, and is derived using
graphical techniques. This checks the N^6 scaling of these terms at first order
by effectively separating the N scaling problem away from the rest of the
physics. The transformation of each binary tensor to the final normal
coordinate basis requires the derivation of Clebsch-Gordon coefficients of S_N
for arbitrary N. This has been accomplished using the group theory of the
symmetric group. This achievement results in an analytic solution for the wave
function, exact through first order, that scales as N^0, effectively
circumventing intensive numerical work. This solution can be systematically
improved with further analytic work by going to yet higher orders in the
perturbation series.Comment: This paper was submitted to the Journal of Mathematical physics, and
is under revie
Feshbach Resonance Cooling of Trapped Atom Pairs
Spectroscopic studies of few-body systems at ultracold temperatures provide
valuable information that often cannot be extracted in a hot environment.
Considering a pair of atoms, we propose a cooling mechanism that makes use of a
scattering Feshbach resonance. Application of a series of time-dependent
magnetic field ramps results in the situation in which either zero, one, or two
atoms remain trapped. If two atoms remain in the trap after the field ramps are
completed, then they have been cooled. Application of the proposed cooling
mechanism to optical traps or lattices is considered.Comment: 5 pages, 3 figures; v.2: major conceptual change
Synthesis and Properties of Dipyridylcyclopentenes
A short and general route to the substituted dipyridylcyclopentenes was explored and several new compounds belonging to this new group of diarylethenes were synthesized. The study of their photochromic and thermochromic properties shows that the rate of the thermal ring opening is strongly dependent on the polarity of the solvent.
Troubles with Bayesianism: An introduction to the psychological immune system
A Bayesian mind is, at its core, a rational mind. Bayesianism is thus well-suited to predict and explain mental processes that best exemplify our ability to be rational. However, evidence from belief acquisition and change appears to show that we do not acquire and update information in a Bayesian way. Instead, the principles of belief acquisition and updating seem grounded in maintaining a psychological immune system rather than in approximating
a Bayesian processor
Analytic, Group-Theoretic Density Profiles for Confined, Correlated N-Body Systems
Confined quantum systems involving identical interacting particles are to
be found in many areas of physics, including condensed matter, atomic and
chemical physics. A beyond-mean-field perturbation method that is applicable,
in principle, to weakly, intermediate, and strongly-interacting systems has
been set forth by the authors in a previous series of papers. Dimensional
perturbation theory was used, and in conjunction with group theory, an analytic
beyond-mean-field correlated wave function at lowest order for a system under
spherical confinement with a general two-body interaction was derived. In the
present paper, we use this analytic wave function to derive the corresponding
lowest-order, analytic density profile and apply it to the example of a
Bose-Einstein condensate.Comment: 15 pages, 2 figures, accepted by Physics Review A. This document was
submitted after responding to a reviewer's comment
Correlation length scalings in fusion edge plasma turbulence computations
The effect of changes in plasma parameters, that are characteristic near or
at an L-H transition in fusion edge plasmas, on fluctuation correlation lengths
are analysed by means of drift-Alfven turbulence computations. Scalings by
density gradient length, collisionality, plasma beta, and by an imposed shear
flow are considered. It is found that strongly sheared flows lead to the
appearence of long-range correlations in electrostatic potential fluctuations
parallel and perpendicular to the magnetic field.Comment: Submitted to "Plasma Physics and Controlled Fusion
Feasibility study of a synthesis procedure for array feeds to improve radiation performance of large distorted reflector antennas
The topics covered include the following: (1) performance analysis of the Gregorian tri-reflector; (2) design and performance of the type 6 reflector antenna; (3) a new spherical main reflector system design; (4) optimization of reflector configurations using physical optics; (5) radiometric array design; and (7) beam efficiency studies
Spectral geometry, homogeneous spaces, and differential forms with finite Fourier series
Let G be a compact Lie group acting transitively on Riemannian manifolds M
and N. Let p be a G equivariant Riemannian submersion from M to N. We show that
a smooth differential form on N has finite Fourier series if and only if the
pull back has finite Fourier series on
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