scholarly journals Conformal basis, optical theorem, and the bulk point singularity

2018 ◽  
Vol 98 (2) ◽  
Author(s):  
Ho Tat Lam ◽  
Shu-Heng Shao
Keyword(s):  
Optical Theorem ◽  
Point Singularity

Single Atom Image Contrast in Fixed Beam Dark Field Electron Microscopy

1974 ◽  
Vol 32 ◽  
pp. 366-367
Author(s):  
Wah Chi
Keyword(s):  
Scattering Amplitude ◽  
Present Report ◽  
Dark Field ◽  
Image Contrast ◽  
Single Atom ◽  
Optical Theorem ◽  
Hartree Fock ◽  
Heavy Atoms ◽  
Beam Stop ◽  
Fixed Beam

Resolution and contrast are the important factors to determine the feasibility of imaging single heavy atoms on a thin substrate in an electron microscope. The present report compares the atom image characteristics in different modes of fixed beam dark field microscopy including the ideal beam stop (IBS), a wire beam stop (WBS), tilted illumination (Tl) and a displaced aperture (DA). Image contrast between one Hg and a column of linearly aligned carbon atoms (representing the substrate), are also discussed. The assumptions in the present calculations are perfectly coherent illumination, atom object is represented by spherically symmetric potential derived from Relativistic Hartree Fock Slater wave functions, phase grating approximation is used to evaluate the complex scattering amplitude, inelastic scattering is ignored, phase distortion is solely due to defocus and spherical abberation, and total elastic scattering cross section is evaluated by the Optical Theorem. The atom image intensities are presented in a Z-modulation display, and the details of calculation are described elsewhere.

scholarly journals CFT unitarity and the AdS Cutkosky rules

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
David Meltzer ◽  
Allic Sivaramakrishnan
Keyword(s):  
Flat Space ◽  
Tree Level ◽  
Optical Theorem ◽  
Conformal Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Weakly Coupled ◽  
S Matrix ◽  
Space Limit ◽  
Diagrammatic Method

Abstract We derive the Cutkosky rules for conformal field theories (CFTs) at weak and strong coupling. These rules give a simple, diagrammatic method to compute the double-commutator that appears in the Lorentzian inversion formula. We first revisit weakly-coupled CFTs in flat space, where the cuts are performed on Feynman diagrams. We then generalize these rules to strongly-coupled holographic CFTs, where the cuts are performed on the Witten diagrams of the dual theory. In both cases, Cutkosky rules factorize loop diagrams into on-shell sub-diagrams and generalize the standard S-matrix cutting rules. These rules are naturally formulated and derived in Lorentzian momentum space, where the double-commutator is manifestly related to the CFT optical theorem. Finally, we study the AdS cutting rules in explicit examples at tree level and one loop. In these examples, we confirm that the rules are consistent with the OPE limit and that we recover the S-matrix optical theorem in the flat space limit. The AdS cutting rules and the CFT dispersion formula together form a holographic unitarity method to reconstruct Witten diagrams from their cuts.

Angle dependent total cross sections and the optical theorem

2001 ◽  
Vol 25 (1) ◽  
pp. 55-67 ◽  
Author(s):  
T.V. Levitina ◽  
E.J. Brändas
Keyword(s):  
Cross Sections ◽  
Optical Theorem ◽  
Total Cross Sections

Modelling of form in thermotropic polymers

1994 ◽  
Vol 348 (1686) ◽  
pp. 73-96 ◽  
Keyword(s):  
Liquid Crystalline ◽  
Main Chain ◽  
Three Dimensional ◽  
Point Singularity ◽  
Dimensional Solution ◽  
Crystalline Polymers ◽  
Elasticity Equations ◽  
Lower Total Energy ◽  
Third Dimension ◽  
Crystalline Microstructure

A lattice model of liquid crystalline microstructure has been developed. It provides the basis for the three-dimensional solution of the Frank elasticity equations for given boundary conditions while, in addition, providing a mechanistic representation of the development of texture as the microstructure relaxes with time. It is also able to represent disclination motion and the processes associated with their interaction. In particular, it has been used to study (s = ± 1/2) disclination loops, both those described by a single rotation vector, 17, and those in which 17 has a constant angular relationship with the loop line and are equivalent to a point singularity at a distance much larger than the loop radius. The application of the model to disclinations of unit strength, which are unstable both energetically and topologically, has shown that the decomposition into two 1/2 strength lines of lower total energy occurs much more readily than topological escape in the third dimension. The implication for structures observed in capillary tubes is discussed. The influence on microstructure of a splay constant much higher than that of twist or bend is explored in the context of main-chain liquid crystalline polymers, in particular, the stabilization of tangential +1 lines under such conditions is predicted in accord with observed microstructural features.

Optical theorem for multipole sources in wave diffraction theory

2016 ◽  
Vol 62 (3) ◽  
pp. 263-268 ◽  
Author(s):  
Yu. A. Eremin ◽  
A. G. Sveshnikov
Keyword(s):  
Wave Diffraction ◽  
Diffraction Theory ◽  
Optical Theorem ◽  
Multipole Sources

A Newton–Marchenko equation and generalized optical theorem for elastodynamics

1992 ◽  
Vol 33 (8) ◽  
pp. 2903-2915 ◽  
Author(s):  
David E. Budreck ◽  
James H. Rose
Keyword(s):  
Optical Theorem ◽  
Marchenko Equation

scholarly journals Generalized optical theorem for reflection, transmission, and extinction of power for electromagnetic fields

2005 ◽  
Vol 71 (5) ◽  
Author(s):  
D. R. Lytle ◽  
P. Scott Carney ◽  
John C. Schotland ◽  
Emil Wolf
Keyword(s):  
Electromagnetic Fields ◽  
Optical Theorem
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