scholarly journals Universality of the Local Spacing Distribution¶in Certain Ensembles of Hermitian Wigner Matrices

2001 ◽  
Vol 215 (3) ◽  
pp. 683-705 ◽  
Author(s):  
Kurt Johansson Johansson
Keyword(s):  
Spacing Distribution ◽  
Wigner Matrices ◽  
Local Spacing

Energies and Electric Dipole Moments of the Bound Vibrational States of HN2+ and DN2+

2008 ◽  
Vol 73 (6-7) ◽  
pp. 873-897 ◽  
Author(s):  
Vladimír Špirko ◽  
Ota Bludský ◽  
Wolfgang P. Kraemer
Keyword(s):  
Dipole Moment ◽  
Nearest Neighbor ◽  
Energy Surface ◽  
Dipole Moments ◽  
Three Dimensional ◽  
Vibrational States ◽  
Spacing Distribution ◽  
Triatomic Molecules ◽  
Vibrational Levels ◽  
Different Levels

The adiabatic three-dimensional potential energy surface and the corresponding dipole moment surface describing the ground electronic state of HN2+ (Χ1Σ+) are calculated at different levels of ab initio theory. The calculations cover the entire bound part of the potential up to its lowest dissociation channel including the isomerization barrier. Energies of all bound vibrational and low-lying ro-vibrational levels are determined in a fully variational procedure using the Suttcliffe-Tennyson Hamiltonian for triatomic molecules. They are in close agreement with the available experimental numbers. From the dipole moment function effective dipoles and transition moments are obtained for all the calculated vibrational and ro-vibrational states. Statistical tools such as the density of states or the nearest-neighbor level spacing distribution (NNSD) are applied to describe and analyse general patterns and characteristics of the energy and dipole results calculated for the massively large number of states of the strongly bound HN2+ ion and its deuterated isotopomer.

Limiting Behavior of Eigenvectors of Large Wigner Matrices

2011 ◽  
Vol 146 (3) ◽  
pp. 519-549 ◽  
Author(s):  
Z. D. Bai ◽  
G. M. Pan
Keyword(s):  
Limiting Behavior ◽  
Wigner Matrices

scholarly journals A Design Approach of Optical Phased Array with Low Side Lobe Level and Wide Angle Steering Range

Photonics ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 63
Author(s):  
Xinyu He ◽  
Tao Dong ◽  
Jingwen He ◽  
Yue Xu
Keyword(s):  
Phased Array ◽  
Phase Distribution ◽  
Beam Steering ◽  
Side Lobe ◽  
Design Approach ◽  
Optical Antennas ◽  
Side Lobe Level ◽  
Wide Angle ◽  
Spacing Distribution ◽  
Optical Phased Array

In this paper, a new design approach of optical phased array (OPA) with low side lobe level (SLL) and wide angle steering range is proposed. This approach consists of two steps. Firstly, a nonuniform antenna array is designed by optimizing the antenna spacing distribution with particle swarm optimization (PSO). Secondly, on the basis of the optimized antenna spacing distribution, PSO is further used to optimize the phase distribution of the optical antennas when the beam steers for realizing lower SLL. Based on the approach we mentioned, we design a nonuniform OPA which has 1024 optical antennas to achieve the steering range of ±60°. When the beam steering angle is 0°, 20°, 30°, 45° and 60°, the SLL obtained by optimizing phase distribution is −21.35, −18.79, −17.91, −18.46 and −18.51 dB, respectively. This kind of OPA with low SLL and wide angle steering range has broad application prospects in laser communication and lidar system.

scholarly journals Equipartition principle for Wigner matrices

2021 ◽  
Vol 9 ◽  
Author(s):  
Zhigang Bao ◽  
László Erdős ◽  
Kevin Schnelli
Keyword(s):  
High Precision ◽  
Quantum Systems ◽  
Wigner Matrices ◽  
Very High

Abstract We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices.

Wigner Matrices and Semicircular Law

2009 ◽  
pp. 15-38 ◽  
Author(s):  
Zhidong Bai ◽  
Jack W. Silverstein
Keyword(s):  
Wigner Matrices ◽  
Semicircular Law

scholarly journals A comment on the Wigner-Dyson-Mehta bulk universality conjecture for Wigner matrices

2012 ◽  
Vol 17 (0) ◽  
Author(s):  
László Erdős ◽  
Horng-Tzer Yau
Keyword(s):  
Wigner Matrices

scholarly journals Local laws for polynomials of Wigner matrices

2020 ◽  
Vol 278 (12) ◽  
pp. 108507
Author(s):  
László Erdős ◽  
Torben Krüger ◽  
Yuriy Nemish
Keyword(s):  
Wigner Matrices

Research on the Idler Spacing of Belt Conveyor

2011 ◽  
Vol 127 ◽  
pp. 295-299 ◽  
Author(s):  
Yong Cun Guo ◽  
Gang Cheng ◽  
Kun Hu ◽  
Zhu Fen Wang
Keyword(s):  
Power Plants ◽  
Minimum Cost ◽  
Belt Conveyor ◽  
Conveyor System ◽  
Spacing Distribution ◽  
Mathematical Expressions ◽  
Crucial Component ◽  
Critical Consideration ◽  
Selection Of ◽  
Conveyor Roller

Belt conveyor is widely used in mine, coal, chemical industry, ports, and power plants. It’s one of the significant devices of continuous conveyor. Roller is a crucial component with regard to belt conveyor system, which supports belts and cargos. In the design of the belt conveyor, a third of major consumption went into rollers. The critical consideration for minimum cost, which including operating, manufacturing, maintenance expenditure, is the selection of idler spacing. For optimization purposes, the optimum pitch between the rollers is regard as more decisive variable, especially for minimizing consumption and reducing rollers’ number than other various factors. This paper discusses the idler spacing to proceed from original technical first, secondly analyzes the effective factors in detail and then deduces rational arrangement mathematical expressions of idler spacing. Simultaneously, combining with the corresponding parameter, we draw up the hierarchical layout figure of idler spacing distribution through the calculation expression. It’s the optimal option of idler spacing that providing an outstanding reference in the actual production.

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