scholarly journals A NEW APPROACH FOR CALCULATING THE MATRIX ELEMENTS OF UNITARY GROUP GENERATOR PRODUCTS

1983 ◽  
Vol 32 (9) ◽  
pp. 1149
Author(s):  
WEN ZHEN-YI
Keyword(s):  
Unitary Group ◽  
Matrix Elements ◽  
Group Generator ◽  
New Approach ◽  
The Matrix

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals SEMICLASSICAL DESCRIPTION OF AVERAGE PAIRING PROPERTIES IN NUCLEI

2011 ◽  
Vol 20 (02) ◽  
pp. 399-405 ◽  
Author(s):  
X. VIÑAS ◽  
P. SCHUCK ◽  
M. FARINE
Keyword(s):  
Size Dependence ◽  
Local Density ◽  
Level Density ◽  
Mean Field ◽  
Matrix Elements ◽  
Fermi Systems ◽  
New Approach ◽  
The Matrix ◽  
The Mean ◽  
Arch Structure

We present a new semiclassical theory for describing pairing in finite Fermi systems. It is based on taking the ħ → 0, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition to the position dependence of the Fermi momentum, the size dependence of the matrix elements of the pairing force is also taken into account in this theory. An example typical for the nuclear situation shows the improvment of this new approach over the standard Local Density Approximation. We also show that if in this approach some shell fluctuations are introduced in the level density, the arch structure displayed by the quantal gaps along isotopic chains is almost recovered. We also point out that in heavy drip line nuclei pairing is strongly reduced.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

scholarly journals Development of High-Performance SiCp/Al-Si Composites by Equal Channel Angular Pressing

Metals ◽  
2018 ◽  
Vol 8 (10) ◽  
pp. 738 ◽  
Author(s):  
Qiong Xu ◽  
Aibin Ma ◽  
Junjie Wang ◽  
Jiapeng Sun ◽  
Jinghua Jiang ◽  
...  
Keyword(s):  
Wear Resistance ◽  
Equal Channel Angular Pressing ◽  
High Performance ◽  
Adhesive Wear ◽  
Processing Route ◽  
Matrix Composites ◽  
New Approach ◽  
Angular Pressing ◽  
The Matrix ◽  
Industry Applications

Relatively low compactness and unsatisfactory uniformity of reinforced particles severely restrict the performance and widespread industry applications of the powder metallurgy (PM) metal matrix composites (MMCs). Here, we developed a combined processing route of PM and equal channel angular pressing (ECAP) to enhance the mechanical properties and wear resistance of the SiCp/Al-Si composite. The results indicate that ECAP significantly refined the matrix grains, eliminated pores and promoted the uniformity of the reinforcement particles. After 8p-ECAP, the SiCp/Al-Si composite consisted of ultrafine Al matrix grains (600 nm) modified by uniformly-dispersed Si and SiCp particles, and the composite relative density approached 100%. The hardness and wear resistance of the 8p-ECAP SiCp/Al-Si composite were markedly improved compared to the PM composite. More ECAP passes continued a trend of improvement for the wear resistance and hardness. Moreover, while abrasion and delamination dominated the wear of PM composites, less severe adhesive wear and fatigue mechanisms played more important roles in the wear of PM-ECAP composites. This study demonstrates a new approach to designing wear-resistant Al-MMCs and is readily applicable to other Al-MMCs.

Sign in / Sign up

Export Citation Format

Share Document