A new uniform asymptotic approximation for the Wigner 6j-symbol is given in terms of Wigner rotation matrices (d-matrices). The approximation is uniform in the sense that it applies for all values of the quantum numbers, even those near caustics. The derivation of the new approximation is not given, but the geometrical ideas supporting it are discussed and numerical tests are presented, including comparisons with the exact 6j-symbol and with the Ponzano-Regge approximation.

Download full-text PDF

Source
http://dx.doi.org/10.1021/jp905056yDOI Listing

Publication Analysis

Top Keywords

approximation wigner
8
wigner 6j-symbol
8
6j-symbol terms
8
rotation matrices
8
approximation
5
uniform semiclassical
4
semiclassical approximation
4
terms rotation
4
matrices uniform
4
uniform asymptotic
4

Similar Publications

In the majority of aerosol drug deposition modelling efforts, the particles are approximated by regular spheres. However, microscope images acquired after drug formulation available in the open literature suggest that their shape is not regular in most of the cases. This work aimed to combine experimental measurements and numerical simulations to reveal the shape factors of the particles of commercialized aerosol drugs and the effect of non-sphericity on the lung deposition distribution of these drugs.

View Article and Find Full Text PDF

Selecting Initial Conditions for Trajectory-Based Nonadiabatic Simulations.

Acc Chem Res

January 2025

Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom.

ConspectusPhotochemical reactions have always been the source of a great deal of mystery. While classified as a type of chemical reaction, no doubts are allowed that the general tenets of ground-state chemistry do not directly apply to photochemical reactions. For a typical chemical reaction, understanding the critical points of the ground-state potential (free) energy surface and embedding them in a thermodynamics framework is often enough to infer reaction yields or characteristic time scales.

View Article and Find Full Text PDF

Typical path integral Monte Carlo approaches use the primitive approximation to compute the probability density for a given path. In this work, we develop the pair discrete variable representation (pair-DVR) approach to study molecular rotations. The pair propagator, which was initially introduced to study superfluidity in condensed helium, is naturally well-suited for systems interacting with a pairwise potential.

View Article and Find Full Text PDF

Objectives: Femtosecond laser image guided high precision trabeculotomy (FLigHT) is a novel open-angle glaucoma treatment. The procedure non-invasively creates aqueous humor (AH) drainage channel from the anterior chamber (AC) to Schlemm's canal (SC) through the trabecular meshwork (TM) to decrease intraocular pressure (IOP). The purpose of this study was to develop a 3D finite element model (FEM) of the FLigHT procedure and to simulate clinical results for different drainage channel cross-sectional areas.

View Article and Find Full Text PDF

The emergence of a local effective theory from a more fundamental theory of quantum gravity with seemingly fewer degrees of freedom is a major puzzle of theoretical physics. A recent approach to this problem is to consider general features of the Hilbert space maps relating these theories. In this work, we construct approximately local observables, or overlapping qubits, from such non-isometric maps.

View Article and Find Full Text PDF

Want AI Summaries of new PubMed Abstracts delivered to your In-box?

Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!