Decoupling of measured spherical tensor components of resolved J states of collisionally excited (Ar)+

1996 ◽  
Vol 74 (11-12) ◽  
pp. 955-958 ◽  
Author(s):  
O. Yenen ◽  
B. W. Moudry ◽  
D. H. Jaecks
Keyword(s):  
Angular Momentum ◽  
Density Matrix ◽  
Nonlinear Equations ◽  
Total Spin ◽  
Reflection Symmetry ◽  
Density Matrices ◽  
Total Orbital Angular Momentum ◽  
Orientation Parameters ◽  
Single Set

We measured Stoke's parameters P1, P2, P3, and P4 of excited Ar+ in coincidence with the scattered He for the two-electron process[Formula: see text]From the measured Stoke's parameters of the 4610 Å (1 Å = 10−10 m) radiation of the 2F(J = 7/2) to the 2D(J = 5/2) transition and the 4590 Å radiation of the 2F(J = 5/2) to 2D(J = 3/2) transition we determined the alignment and orientation parameters of the upper states using the Fano–Macek formalism. These parameters were then converted to the appropriate spherical tensor components in the J representation to obtain, in general eight values of [Formula: see text]. Since these states are best described by LS coupling, we decoupled the spherical tensor components of the density matrix of each J state in terms of the spherical components of the density matrices of the total orbital angular momentum L and total spin 5. The unknowns in the expansion are [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], with [Formula: see text] because of reflection symmetry. We used Mathematica to calculate the decoupling coefficients and solve these nonlinear equations. The decoupling also allows us to optically determine the octopole moments of the total orbital momentum provided that [Formula: see text] is nonzero. When [Formula: see text], the two sets of equations are linearly dependent. In this case, the determination of a single set of [Formula: see text] specifies [Formula: see text].

scholarly journals Insights into one-body density matrices using deep learning

2020 ◽  
Vol 224 ◽  
pp. 265-291 ◽  
Author(s):  
Jack Wetherell ◽  
Andrea Costamagna ◽  
Matteo Gatti ◽  
Lucia Reining
Keyword(s):  
Deep Learning ◽  
Density Matrix ◽  
Reduced Density Matrix ◽  
Body Density ◽  
Density Matrices ◽  
Learning Constraints ◽  
The One ◽  
Reduced Density

Deep-learning constraints of the one-body reduced density matrix from its compressibility to enable efficient determination of key observables.

Basis states for equivalent electrons. II. States for the Lie group Sp(4l + 2)

1980 ◽  
Vol 58 (12) ◽  
pp. 1724-1728
Author(s):  
William R. Ross
Keyword(s):  
Angular Momentum ◽  
Irreducible Representation ◽  
Orbital Angular Momentum ◽  
Lie Group ◽  
Total Spin ◽  
Irreducible Representations ◽  
Total Orbital Angular Momentum ◽  
Intermediate Group ◽  
Slater Basis

The Slater basis states for N equivalent electrons form the basis for the irreducible representation (1N) of the Lie group U(4l + 2). States which are eigenfunctions of the total spin and total orbital angular momentum form the basis for irreducible representations of SO(3) × SU(2). In this paper the intermediate group Sp(4l + 2) is studied. The basis states for irreducible representations of Sp(4l + 2) are expressed in terms of the Slater basis states.

Orbital angular momentum eigenfunctions for many-particle systems

1985 ◽  
Vol 63 (7) ◽  
pp. 1719-1722 ◽  
Author(s):  
John Avery
Keyword(s):  
Angular Momentum ◽  
Symmetric Group ◽  
Orbital Angular Momentum ◽  
Particle System ◽  
Total Spin ◽  
Particle Systems ◽  
Irreducible Representations ◽  
Angular Momentum Operator ◽  
Total Orbital Angular Momentum ◽  
Orbital Angular Momentum Operator

Methods are presented for constructing eigenfunctions of the total orbital angular momentum operator of a many-particle system without the use of the Clebsch–Gordan coefficients. One of the equations derived in this paper is analogous to Dirac's identity for total spin; and through this equation, a connection is established between eigenfunctions of L2 and irreducible representations of the symmetric group Sn.

scholarly journals Evaluation of hydrological and cryospheric angular momentum estimates based on GRACE, GRACE-FO and SLR data for their contributions to polar motion excitation

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Justyna Śliwińska ◽  
Jolanta Nastula ◽  
Małgorzata Wińska
Keyword(s):  
Angular Momentum ◽  
Spherical Harmonic ◽  
Polar Motion ◽  
Spectral Band ◽  
Water Storage ◽  
Terrestrial Water Storage ◽  
Terrestrial Water ◽  
High Consistency ◽  
Polar Motion Excitation

AbstractIn geodesy, a key application of data from the Gravity Recovery and Climate Experiment (GRACE), GRACE Follow-On (GRACE-FO), and Satellite Laser Ranging (SLR) is an interpretation of changes in polar motion excitation due to variations in the Earth’s surficial fluids, especially in the continental water, snow, and ice. Such impacts are usually examined by computing hydrological and cryospheric polar motion excitation (hydrological and cryospheric angular momentum, HAM/CAM). Three types of GRACE and GRACE-FO data can be used to determine HAM/CAM, namely degree-2 order-1 spherical harmonic coefficients of geopotential, gridded terrestrial water storage anomalies computed from spherical harmonic coefficients, and terrestrial water storage anomalies obtained from mascon solutions. This study compares HAM/CAM computed from these three kinds of gravimetric data. A comparison of GRACE-based excitation series with HAM/CAM obtained from SLR is also provided. A validation of different HAM/CAM estimates is conducted here using the so-called geodetic residual time series (GAO), which describes the hydrological and cryospheric signal in the observed polar motion excitation. Our analysis of GRACE mission data indicates that the use of mascon solutions provides higher consistency between HAM/CAM and GAO than the use of other datasets, especially in the seasonal spectral band. These conclusions are confirmed by the results obtained for data from first 2 years of GRACE-FO. Overall, after 2 years from the start of GRACE-FO, the high consistency between HAM/CAM and GAO that was achieved during the best GRACE period has not yet been repeated. However, it should be remembered that with the systematic appearance of subsequent GRACE-FO observations, this quality can be expected to increase. SLR data can be used for determination of HAM/CAM to fill the one-year-long data gap between the end of GRACE and the start of the GRACE-FO mission. In addition, SLR series could be particularly useful in determination of HAM/CAM in the non-seasonal spectral band. Despite its low seasonal amplitudes, SLR-based HAM/CAM provides high phase consistency with GAO for annual and semiannual oscillation.

N-Representable one-electron reduced density matrices reconstruction at non-zero temperatures

2021 ◽  
Vol 77 (5) ◽  
Author(s):  
Yoann Launay ◽  
Jean-Michel Gillet
Keyword(s):  
Density Matrix ◽  
Thermal Effects ◽  
Scattering Data ◽  
Temperature Dependent ◽  
Density Matrices ◽  
Reduced Density Matrices ◽  
Structure Factors ◽  
Reduced Density ◽  
Statistical Noise

This article retraces different methods that have been explored to account for the atomic thermal motion in the reconstruction of one-electron reduced density matrices from experimental X-ray structure factors (XSF) and directional Compton profiles (DCP). Attention has been paid to propose the simplest possible model, which obeys the necessary N-representability conditions, while accurately reproducing all available experimental data. The deconvolution of thermal effects makes it possible to obtain an experimental static density matrix, which can directly be compared with theoretical 1-RDM (reduced density matrix). It is found that above a 1% statistical noise level, the role played by Compton scattering data becomes negligible and no accurate 1-RDM is reachable. Since no thermal 1-RDM is available as a reference, the quality of an experimentally derived temperature-dependent matrix is difficult to assess. However, the accuracy of the obtained static 1-RDM, through the performance of the refined observables, is strong evidence that the Semi-Definite Programming method is robust and well adapted to the reconstruction of an experimental dynamical 1-RDM.

scholarly journals The Relativistic and the Hidden Momentum of Minkowski and Abraham in Relativistic Energy Wave

2021 ◽  
Author(s):  
Daniel Cardoso
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Mechanical Energy ◽  
Recent Theory ◽  
Translational Energy ◽  
Angle Of Incidence ◽  
Relativistic Energy ◽  
Conservation Of Energy ◽  
Ignition Device

An analysis of the consistency of the Abraham and Minkowski momenta in the determination of the photon trajectory was carried out considering a new principle of conservation of the photon's mechanical energy, in which the photon conserves translational energy in orbital angular momentum when transiting between two media, introducing the relativistic energy wave (REW). The confrontation between REW and the recent theory of space-time waves (ST) was considered, pondering your differences. Throughout this study it was possible to verify that the Abraham momentum appears a relativistic photon ignition device in the transition between two media, acting as the hidden momentum of the Minkowski’s relativistic momentum. The wavy behavior in the matter is relativistic, and the relativistic trajectory appears with delays and advances, with points of synchronization between source-observer. The classical or relativistic trajectories are determined as a function of the angle of incidence and the relative refractive index, by one of two distinct non-additive torques, the classic by Abraham or the relativistic by Minkowski. It was found that the same analysis conducted under the principle of conservation of the mechanical energy of the photon can be treated by an new Doppler, Relativistic Apparent, that can be confused with other Dopplers in the treatment of redshift from distant sources. It was found that the conservation of energy in Orbital Angular Momentum (OAM), in the interaction with matter, explains that the synchronization instants are found in the inversion of the OAM, where the advances and delays of REW occur under negligible variations of the OAM, however, opposites.

ON THE DETERMINATION OF CAUSTICS

2004 ◽  
Vol 03 (01) ◽  
pp. 91-102 ◽  
Author(s):  
PONMILE OLOYEDE ◽  
GENNADY MIL'NIKOV ◽  
HIROKI NAKAMURA
Keyword(s):  
Angular Momentum ◽  
Numerical Method ◽  
Total Angular Momentum ◽  
Reaction Process ◽  
Classical Trajectories ◽  
Arbitrary Dimensions

This paper presents a numerical method which locates caustics of classical trajectories on-the-fly. The method is conceptually simple and is applicable to a system of arbitrary dimensions. The efficiency of the method is demonstrated by determining caustics of trajectories in the 2-D Henon–Heiles potential and of trajectories used to simulate a triatomic reaction process for J (total angular momentum) = 0.

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