Dynamical equations for a Regge theory with crossing symmetry and unitarity. II. The case of strong coupling, and elimination of ghost poles

1977 ◽  
Vol 15 (8) ◽  
pp. 2366-2385 ◽  
Author(s):  
Porter W. Johnson ◽  
Robert L. Warnock
Keyword(s):  
Strong Coupling ◽  
Dynamical Equations ◽  
Regge Theory ◽  
Crossing Symmetry

Application of Modified Bloch Waves to Image Analysis of Extended Linear Defects

1974 ◽  
Vol 32 ◽  
pp. 402-403
Author(s):  
S. Nakahara ◽  
D. M. Maher
Keyword(s):  
Image Analysis ◽  
Computational Approach ◽  
Dislocation Loops ◽  
Plane Wave Expansion ◽  
Dynamical Equations ◽  
Bloch Waves ◽  
Linear Defects ◽  
Imperfect Crystal ◽  
Localized Defects ◽  
Defective Crystals

Since Head first demonstrated the advantages of computer displayed theoretical intensities from defective crystals, computer display techniques have become important in image analysis. However the computational methods employed resort largely to numerical integration of the dynamical equations of electron diffraction. As a consequence, the interpretation of the results in terms of the defect displacement field and diffracting variables is difficult to follow in detail. In contrast to this type of computational approach which is based on a plane-wave expansion of the excited waves within the crystal (i.e. Darwin representation ), Wilkens assumed scattering of modified Bloch waves by an imperfect crystal. For localized defects, the wave amplitudes can be described analytically and this formulation has been used successfully to predict the black-white symmetry of images arising from small dislocation loops.

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

2019 ◽  
Author(s):  
S. Giarrusso ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Strong Coupling ◽  
Density Functional ◽  
Correlation Energy ◽  
Order Term ◽  
Strong Coupling Limit ◽  
Local Form ◽  
Coupling Constant ◽  
Functional Theory ◽  
Exchange Correlation

We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

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