scholarly journals Collective motion of two-electron atom in hyperspherical adiabatic approximation

2015 ◽  
Author(s):  
A. S. Mohamed ◽  
S. I. Nikitin
Keyword(s):  
Adiabatic Approximation ◽  
Collective Motion ◽  
Electron Atom ◽  
Hyperspherical Adiabatic

QUALITY OF HYPERSPHERICAL ADIABATIC APPROXIMATION FOR EXCITED STATES OF ATOMIC SYSTEMS

2004 ◽  
Vol 19 (29) ◽  
pp. 4973-4984 ◽  
Author(s):  
TAPAN KUMAR DAS ◽  
BARNALI CHAKRABARTI
Keyword(s):  
Excited States ◽  
Adiabatic Approximation ◽  
Invariance Condition ◽  
Constant Matrix ◽  
Shape Invariance ◽  
Atomic Systems ◽  
Potential Matrix ◽  
Hyperspherical Adiabatic ◽  
Common Function

We calculate ground and several low-lying excited states of various two electron atoms using hyperspherical adiabatic approximation (HAA). Its spectracular accuracy, as compared to exact numerical results of a set of coupled differential equations, demands a better understanding of its mechanism. It is seen that factorizability of the potential matrix into a product of a common function of the global length (hyperradius) and a constant matrix, is responsible for this remarkable success. This is a result of the shape invariance condition in multidimensional supersymmetric quantum mechanics.

Electron-Atom Collisions

1995 ◽  
Author(s):  
Ian E. McCarthy ◽  
Erich Weigold
Keyword(s):  
Electron Atom

Local interaction rules and collective motion in black neon tetra (Hyphessobrycon herbertaxelrodi) and zebrafish (Danio rerio).

2019 ◽  
Vol 133 (2) ◽  
pp. 143-155 ◽  
Author(s):  
Vicenç Quera ◽  
Elisabet Gimeno ◽  
Francesc S. Beltran ◽  
Ruth Dolado
Keyword(s):  
Danio Rerio ◽  
Collective Motion ◽  
Local Interaction

RELAXATION AND COLLECTIVE MOTION IN SUPERCONDUCTORS. A TWO-FLUID DESCRIPTION

1978 ◽  
Vol 39 (C6) ◽  
pp. C6-488-C6-489 ◽  
Author(s):  
C. J. Pethick ◽  
H. Smith
Keyword(s):  
Collective Motion ◽  
Two Fluid

Analysis of the Bath Motion in the MM-SQC Dynamics Using Unsupervised Machine Learning Dimensionality Reduction Approaches: Principal Component Analysis

2020 ◽  
Author(s):  
Jiawei Peng ◽  
Yu Xie ◽  
Deping Hu ◽  
Zhenggang Lan
Keyword(s):  
Machine Learning ◽  
Principal Component Analysis ◽  
Collective Motion ◽  
Principal Component ◽  
Component Analysis ◽  
Nonadiabatic Dynamics ◽  
Trajectory Data ◽  
Unsupervised Machine Learning ◽  
Physical Knowledge ◽  
Vibronic Couplings

The system-plus-bath model is an important tool to understand nonadiabatic dynamics for large molecular systems. The understanding of the collective motion of a huge number of bath modes is essential to reveal their key roles in the overall dynamics. We apply the principal component analysis (PCA) to investigate the bath motion based on the massive data generated from the MM-SQC (symmetrical quasi-classical dynamics method based on the Meyer-Miller mapping Hamiltonian) nonadiabatic dynamics of the excited-state energy transfer dynamics of Frenkel-exciton model. The PCA method clearly clarifies that two types of bath modes, which either display the strong vibronic couplings or have the frequencies close to electronic transition, are very important to the nonadiabatic dynamics. These observations are fully consistent with the physical insights. This conclusion is obtained purely based on the PCA understanding of the trajectory data, without the large involvement of pre-defined physical knowledge. The results show that the PCA approach, one of the simplest unsupervised machine learning methods, is very powerful to analyze the complicated nonadiabatic dynamics in condensed phase involving many degrees of freedom.

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