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

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

Statistical reliability of meta_analysis research claims for gas stove cooking_childhood respiratory health associations

Odds ratios or p_values from individual observational studies can be combined to examine a common cause_effect research question in meta_analysis. However, reliability of individual studies used in meta_analysis should not be taken for granted as claimed cause_effect associations may not reproduce. An evaluation was undertaken on meta_analysis of base papers examining gas stove cooking, including nitrogen dioxide, NO2, and childhood asthma and wheeze associations. Numbers of hypotheses tested in 14 of 27 base papers, 52 percent, used in meta_analysis of asthma and wheeze were counted. Test statistics used in the meta_analysis, 40 odds ratios with 95 percent confidence limits, were converted to p_values and presented in p_value plots. The median and interquartile range of possible numbers of hypotheses tested in the 14 base papers was 15,360, 6,336_49,152. None of the 14 base papers made mention of correcting for multiple testing, nor was any explanation offered if no multiple testing procedure was used. Given large numbers of hypotheses available, statistics drawn from base papers and used for meta-analysis are likely biased. Even so, p-value plots for gas stove_current asthma and gas stove_current wheeze associations show randomness consistent with unproven gas stove harms. The meta-analysis fails to provide reliable evidence for public health policy making on gas stove harms to children in North America. NO2 is not established as a biologically plausible explanation of a causal link with childhood asthma. Biases_multiple testing and p-hacking_cannot be ruled out as explanations for a gas stove_current asthma association claim. Selective reporting is another bias in published literature of gas stove_childhood respiratory health studies. Keywords gas stove, asthma, meta-analysis, p-value plot, multiple testing, p_hackingComment: International Journal of Statistics and Probability (2023

Colour Relations in Form

The orthodox monadic determination thesis holds that we represent colour relations by virtue of representing colours. Against this orthodoxy, I argue that it is possible to represent colour relations without representing any colours. I present a model of iconic perceptual content that allows for such primitive relational colour representation, and provide four empirical arguments in its support. I close by surveying alternative views of the relationship between monadic and relational colour representation