Solution of the Single-Site Aspherical Scattering Problem for the Dirac Equation

1991 ◽  
Vol 253 ◽  
Author(s):  
Stephen C. Lovatt ◽  
B.L. Gyorffy ◽  
Guang-Yu Guo
Keyword(s):  
Dirac Equation ◽  
Partial Wave ◽  
Wave Scattering ◽  
Crystalline Silicon ◽  
Scattering Problem ◽  
Scattering Matrix ◽  
Single Site ◽  
Finite Range ◽  
S Matrix

ABSTRACTWe study the scattering solutions of the Dirac equation numerically for anisotropic, finite range (warped muffin-tin), potentials. In particular, we calculate the partial-wave scattering matrix, ƒAA'(ε) and S-matrix SAA′(ε), for a potential characteristic of crystalline Silicon. We illustrate the consequences of aspherical scattering with reference to Silicon.

Subwavelength Defect Characterization Using Guided Wave Scattering Matrix

2013 ◽  
Vol 330 ◽  
pp. 504-509
Author(s):  
Yang Zheng ◽  
Jin Jie Zhou ◽  
Hui Zheng
Keyword(s):  
Wave Scattering ◽  
Scattering Matrix ◽  
Guided Wave ◽  
Defect Characterization ◽  
Challenging Problem ◽  
Recognition Method ◽  
Quantitative Characterization ◽  
S Matrix ◽  
Imaging Algorithms

Although many imaging algorithms such as ellipse and hyperbola algorithm can roughly locate defects in large plate-like structures with sparse guided wave arrays, quantitative characterization of them is still a challenging problem, especially for those small defects known as subwavelength defects. Scattering signals of defects contain abundant information so that can be used to evaluate defects. A defects recognition method using the S-matrix (scattering matrix) was presented. S-matrices of hole and crack with S0 mode incident were experimentally measured. The results show that defects can be recognized from the morphology of 2D S-matrix chart. This method has great potential to achieve more specific parameters of small defects with sparse guided wave arrays.

INTEGRABLE MODELS OF FIELD THEORY AND SCATTERING ON QUANTUM HYPERBOLOIDS

1992 ◽  
Vol 07 (05) ◽  
pp. 441-446 ◽  
Author(s):  
A. ZABRODIN
Keyword(s):  
Field Theory ◽  
Symmetric Space ◽  
Quantum Group ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Free Particle ◽  
Compact Quantum Group ◽  
Integrable Models ◽  
S Wave

We consider the scattering of two dressed excitations in the antiferromagnetic XXZ spin-1/2 chain and show that it is equivalent to the S-wave scattering problem for a free particle on the certain quantum symmetric space “quantum hyperboloid” related to the non-compact quantum group SU q (1, 1).

scholarly journals Flow of S-matrix poles for elementary quantum potentials1This research was supported in part by an NSERC Undergraduate Summer Research Award (SGN) and an NSERC Discovery Grant (MAW).

2011 ◽  
Vol 89 (11) ◽  
pp. 1127-1140 ◽  
Author(s):  
B. Belchev ◽  
S.G. Neale ◽  
M.A. Walton
Keyword(s):  
Bound States ◽  
Scattering Matrix ◽  
Nucl Phys ◽  
Quantum Scattering ◽  
Research Award ◽  
Momentum Plane ◽  
S Matrix ◽  
Potential Depth ◽  
Square Well ◽  
Insight Into

The poles of the quantum scattering matrix (S-matrix) in the complex momentum plane have been studied extensively. Bound states give rise to S-matrix poles, and other poles correspond to non-normalizable antibound, resonance, and antiresonance states. They describe important physics but their locations can be difficult to determine. In pioneering work, Nussenzveig (Nucl. Phys. 11, 499 (1959)) performed the analysis for a square well (wall), and plotted the flow of the poles as the potential depth (height) varied. More than fifty years later, however, little has been done in the way of direct generalization of those results. We point out that today we can find such poles easily and efficiently using numerical techniques and widely available software. We study the poles of the scattering matrix for the simplest piecewise flat potentials, with one and two adjacent (nonzero) pieces. For the finite well (wall) the flow of the poles as a function of the depth (height) recovers the results of Nussenzveig. We then analyze the flow for a potential with two independent parts that can be attractive or repulsive, the two-piece potential. These examples provide some insight into the complicated behavior of the resonance, antiresonance, and antibound poles.

scholarly journals THE VIRTUAL BLACK HOLE IN 2D QUANTUM GRAVITY AND ITS RELEVANCE FOR THE S-MATRIX

2002 ◽  
Vol 17 (06n07) ◽  
pp. 989-992 ◽  
Author(s):  
DANIEL GRUMILLER
Keyword(s):  
Black Hole ◽  
Quantum Gravity ◽  
Wave Scattering ◽  
Black Hole Mass ◽  
Hole Formation ◽  
S Wave ◽  
Scalar Matter ◽  
S Matrix ◽  
Tree Vertex ◽  
Classical Mechanism

As shown recently 2d quantum gravity theories — including spherically reduced Einstein-gravity — after an exact path integral of its geometric part can be treated perturbatively in the loops of (scalar) matter. Obviously the classical mechanism of black hole formation should be contained in the tree approximation of the theory. This is shown to be the case for the scattering of two scalars through an intermediate state which by its effective black hole mass is identified as a "virtual black hole". We discuss the lowest order tree vertex for minimally and non-minimally coupled scalars and find a non-trivial finite S-matrix for gravitational s-wave scattering in the latter case.

High sensitive detection of high-order partial wave scattering in photoassociation of ultracold atoms

2012 ◽  
Vol 21 (4) ◽  
pp. 043404 ◽  
Author(s):  
Yu-Qing Li ◽  
Jie Ma ◽  
Ji-Zhou Wu ◽  
Yi-Chi Zhang ◽  
Yan-Ting Zhao ◽  
...  
Keyword(s):  
Partial Wave ◽  
Wave Scattering ◽  
Ultracold Atoms ◽  
High Order ◽  
Sensitive Detection
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