General methods for evaluating matrix elements of singular operators in two-electron systems

1994 ◽  
Vol 72 (11-12) ◽  
pp. 822-844 ◽  
Author(s):  
Zong-Chao Yan ◽  
G. W. F. Drake
Keyword(s):  
General Scheme ◽  
Triplet States ◽  
Electron Systems ◽  
Matrix Elements ◽  
Atomic Systems ◽  
Singular Operators ◽  
Wide Range ◽  
Qed Effects ◽  
Hylleraas Coordinates ◽  
Theory And Experiment

Due to the recent advances in both theory and experiment for the fine structure of two-electron atomic systems, it is necessary to include quantum electrodynamic (QED) effects through orders α6mc2, α7ln(Zα)mc2, and α7mc2, in order to match the experimental precision. These effects can be expressed in terms of a sum of singular operators. A general scheme is given for the evaluation of a wide range of matrix elements of high-order singular QED operators for two-electron atomic systems in Hylleraas coordinates. The scheme presented here can be applied to triplet states with arbitrary angular momentum. A number of useful expressions for the analytical evaluation of radial integrals are derived. An example is given in calculating the Douglas and Kroll terms, and the numerical values of the reduced matrix elements are presented for the 2 3PJ states of helium.

scholarly journals Soft-drop grooming for hadronic event shapes

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Jeremy Baron ◽  
Daniel Reichelt ◽  
Steffen Schumann ◽  
Niklas Schwanemann ◽  
Vincent Theeuwes
Keyword(s):  
Event Generator ◽  
Experimental Measurements ◽  
Event Shape ◽  
Matrix Elements ◽  
Underlying Event ◽  
Hadronic Event ◽  
Wide Range ◽  
Event Shapes ◽  
The Impact ◽  
Perturbative Corrections

Abstract Soft-drop grooming of hadron-collision final states has the potential to significantly reduce the impact of non-perturbative corrections, and in particular the underlying-event contribution. This eventually will enable a more direct comparison of accurate perturbative predictions with experimental measurements. In this study we consider soft-drop groomed dijet event shapes. We derive general results needed to perform the resummation of suitable event-shape variables to next-to-leading logarithmic (NLL) accuracy matched to exact next-to-leading order (NLO) QCD matrix elements. We compile predictions for the transverse-thrust shape accurate to NLO + NLL′ using the implementation of the Caesar formalism in the Sherpa event generator framework. We complement this by state-of-the-art parton- and hadron-level predictions based on NLO QCD matrix elements matched with parton showers. We explore the potential to mitigate non-perturbative corrections for particle-level and track-based measurements of transverse thrust by considering a wide range of soft-drop parameters. We find that soft-drop grooming indeed is very efficient in removing the underlying event. This motivates future experimental measurements to be compared to precise QCD predictions and employed to constrain non-perturbative models in Monte-Carlo simulations.

Systematic calculations of energy levels and transitions rates in Mo XXVIII

2020 ◽  
Vol 75 (8) ◽  
pp. 739-747
Author(s):  
Feng Hu ◽  
Yan Sun ◽  
Maofei Mei
Keyword(s):  
Energy Levels ◽  
Oscillator Strengths ◽  
Atomic Data ◽  
Data Sets ◽  
Electron Systems ◽  
Excitation Energies ◽  
Experimental Values ◽  
Qed Effects ◽  
Hyperfine Structures ◽  
Good Agreement

AbstractComplete and consistent atomic data, including excitation energies, lifetimes, wavelengths, hyperfine structures, Landé gJ-factors and E1, E2, M1, and M2 line strengths, oscillator strengths, transitions rates are reported for the low-lying 41 levels of Mo XXVIII, belonging to the n = 3 states (1s22s22p6)3s23p3, 3s3p4, and 3s23p23d. High-accuracy calculations have been performed as benchmarks in the request for accurate treatments of relativity, electron correlation, and quantum electrodynamic (QED) effects in multi-valence-electron systems. Comparisons are made between the present two data sets, as well as with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology wherever available. The calculated values including core-valence correction are found to be in a good agreement with other theoretical and experimental values. The present results are accurate enough for identification and deblending of emission lines involving the n = 3 levels, and are also useful for modeling and diagnosing plasmas.

scholarly journals Erratum: Nonradiative α7m QED effects in the Lamb shift of helium triplet states [Phys. Rev. A 101 , 062516 (2020)]

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Vojtěch Patkóš ◽  
Vladimir A. Yerokhin ◽  
Krzysztof Pachucki
Keyword(s):  
Lamb Shift ◽  
Triplet States ◽  
Qed Effects

scholarly journals Semiclassical calculations of the quadruple excited four-electron systems

2007 ◽  
pp. 33-44
Author(s):  
N. Simonovic ◽  
M. Predojevic ◽  
V. Pankovic ◽  
P. Grujic
Keyword(s):  
Energy Levels ◽  
Point Of View ◽  
Interstellar Space ◽  
Vibrational Modes ◽  
Electron Systems ◽  
Atomic Systems ◽  
Excited Atoms ◽  
Relative Contribution ◽  
Quantum Numbers ◽  
Semiclassical States

Highly excited atoms acquire very large dimensions and can be present only in a very rarified gas medium, such as the interstellar space. Multiply excited beryllium-like systems, when excited to large principal quantum numbers, have a radius of r ? 10 ?. We examine the semiclassical spectrum of quadruple highly excited four-electron atomic systems for the plane model of equivalent electrons. The energy of the system consists of rotational and vibrational modes within the almost circular orbit approximation, as used in a previous calculation for the triply excited three-electron systems. Here we present numerical results for the beryllium atom. The lifetimes of the semiclassical states are estimated via the corresponding Lyapunov exponents. The vibrational modes relative contribution to the energy levels rises with the degree of the Coulombic excitation. The relevance of the results is discussed both from the observational and heuristic point of view.

Orbit–orbit interaction inn fN electron configurations

1969 ◽  
Vol 47 (17) ◽  
pp. 1885-1888 ◽  
Author(s):  
K. M. S. Saxena ◽  
G. Malli
Keyword(s):  
Orbit Interaction ◽  
Matrix Elements ◽  
Atomic Systems ◽  
Hartree Fock ◽  
The Matrix

The expressions of the matrix elements of the orbit–orbit interaction for various fN electron configurations are computed and tabulated for general usage. These expressions are used to evaluate the Hartree–Fock values of the orbit–orbit interaction in all the states for a large number of fN electron atomic systems.

Music Onset Detection

2010 ◽  
pp. 297-316
Author(s):  
Ruohua Zhou ◽  
Josh D Reiss
Keyword(s):  
Performance Measures ◽  
Essential Role ◽  
General Scheme ◽  
Future Research ◽  
Onset Detection ◽  
Time Frequency ◽  
Detection Algorithms ◽  
Music Signal ◽  
Wide Range ◽  
Future Research Directions

Music onset detection plays an essential role in music signal processing and has a wide range of applications. This chapter provides a step by step introduction to the design of music onset detection algorithms. The general scheme and commonly-used time-frequency analysis for onset detection are introduced. Many methods are reviewed, and some typical energy-based, phase-based, pitch-based and supervised learning methods are described in detail. The commonly used performance measures, onset annotation software, public database and evaluation methods are introduced. The performance difference between energy-based and pitch-based method is discussed. The future research directions for music onset detection are also described.

The Changing Views of a Philosopher of Chemistry on the Question of Reduction

2016 ◽  
Author(s):  
Eric R. Scerri
Keyword(s):  
Quantum Mechanics ◽  
Mathematical Theory ◽  
Approximate Solutions ◽  
Electron Systems ◽  
Atomic Systems ◽  
Quantum Mechanical Description ◽  
The Subject ◽  
The Moment ◽  
The Relationship

The question of the reduction of chemistry to quantum mechanics has been inextricably linked with the development of the philosophy of chemistry since the field began to develop in the early 1990s. In the present chapter I would like to describe how my own views on the subject have developed over a period of roughly 30 years. A good place to begin might be the frequently cited reductionist dictum that was penned in 1929 by Paul Dirac, one of the founders of quantum mechanics. . . . The underlying laws necessary for the mathematical theory of a larger part of physics and the whole of chemistry are thus completely known, and the difficulty is only that exact applications of these laws lead to equations, which are too complicated to be soluble. (Dirac 1929) . . . These days most chemists would probably comment that Dirac had things backward. It is clear that nothing like “the whole of chemistry” has been mathematically understood. At the same time most would argue that the approximate solutions that are afforded by modern computers are so good as to overcome the fact that one cannot obtain exact or analytical solutions to the Schrödinger equation for many-electron systems. Be that as it may, Dirac’s famous quotation, coming from one of the creators of quantum mechanics, has convinced many people that chemistry has been more or less completely reduced to quantum mechanics. Another quotation of this sort (and one using more metaphorical language) comes from Walter Heitler who together with Fritz London was the first to give a quantum mechanical description of the chemical bond. . . . Let us assume for the moment that the two atomic systems ↑↑↑↑ . . . and ↓↓↓↓ . . . are always attracted in a homopolar manner. We can, then, eat Chemistry with a spoon. (Heitler 1927) . . . Philosophers of science eventually caught up with this climate of reductionism and chose to illustrate their views with the relationship with chemistry and quantum mechanics.

scholarly journals Monte Carlo Study of Electronic Transport in Monolayer InSe

Materials ◽  
2019 ◽  
Vol 12 (24) ◽  
pp. 4210 ◽  
Author(s):  
Sanjay Gopalan ◽  
Gautam Gaddemane ◽  
Maarten L. Van de Put ◽  
Massimo V. Fischetti
Keyword(s):  
Monte Carlo ◽  
Long Range ◽  
Electron Mobility ◽  
Short Range ◽  
Field Effect Transistors ◽  
2D Materials ◽  
Matrix Elements ◽  
Electronic Band ◽  
Low Field ◽  
Wide Range

The absence of a band gap in graphene makes it of minor interest for field-effect transistors. Layered metal chalcogenides have shown great potential in device applications thanks to their wide bandgap and high carrier mobility. Interestingly, in the ever-growing library of two-dimensional (2D) materials, monolayer InSe appears as one of the new promising candidates, although still in the initial stage of theoretical studies. Here, we present a theoretical study of this material using density functional theory (DFT) to determine the electronic band structure as well as the phonon spectrum and electron-phonon matrix elements. The electron-phonon scattering rates are obtained using Fermi’s Golden Rule and are used in a full-band Monte Carlo computer program to solve the Boltzmann transport equation (BTE) to evaluate the intrinsic low-field mobility and velocity-field characteristic. The electron-phonon matrix elements, accounting for both long- and short-range interactions, are considered to study the contributions of different scattering mechanisms. Since monolayer InSe is a polar piezoelectric material, scattering with optical phonons is dominated by the long-range interaction with longitudinal optical (LO) phonons while scattering with acoustic phonons is dominated by piezoelectric scattering with the longitudinal (LA) branch at room temperature (T = 300 K) due to a lack of a center of inversion symmetry in monolayer InSe. The low-field electron mobility, calculated considering all electron-phonon interactions, is found to be 110 cm2V−1s−1, whereas values of 188 cm2V−1s−1 and 365 cm2V−1s−1 are obtained considering the long-range and short-range interactions separately. Therefore, the calculated electron mobility of monolayer InSe seems to be competitive with other previously studied 2D materials and the piezoelectric properties of monolayer InSe make it a suitable material for a wide range of applications in next generation nanoelectronics.

A Method of Predicting Moments of Market Trend Reversal for Decision-Making Block of Computer-Based Intelligent Financial Agent-Avatar

2020 ◽  
pp. 1-18
Author(s):  
Vsevolod Chernyshenko ◽  
Vladimir Soloviev ◽  
Vadim Feklin ◽  
Mikhail Koroteev ◽  
Nikita Titov
Keyword(s):  
General Scheme ◽  
Classification Algorithm ◽  
Learning Tools ◽  
Financial Indicators ◽  
Economic Time Series ◽  
Wide Range ◽  
Economic Time ◽  
Computer Based ◽  
Market Trends ◽  
Traditional Approaches

The chapter formalizes the financial task for the definitions and properties of financial indicators under study. A wide range of traditional approaches used for predicting economic time series were reviewed. Investigated as well were the advanced algorithms for predicting moments of reversals of market trends based on machine learning tools. The chapter discusses the effectiveness of different kinds of approaches, which is illustrated with related examples. Described is an original securities price dynamics trend classification algorithm, based on the use of the sliding window methodology and financial agents. General scheme of the classification algorithm to identify market phases is analyzed and results of computer modeling are presented. Selection of initial and resulting metrics is grounded.

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