scholarly journals Dual S-matrix bootstrap. Part I. 2D theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Andrea L. Guerrieri ◽  
Alexandre Homrich ◽  
Pedro Vieira
Keyword(s):  
Optimization Theory ◽  
Scattering Matrix ◽  
Dual Approach ◽  
Physical Systems ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Primal Formulation ◽  
Rigorous Bounds ◽  
Duality In Optimization ◽  
Stable Particles

Abstract Using duality in optimization theory we formulate a dual approach to the S-matrix bootstrap that provides rigorous bounds to 2D QFT observables as a consequence of unitarity, crossing symmetry and analyticity of the scattering matrix. We then explain how to optimize such bounds numerically, and prove that they provide the same bounds obtained from the usual primal formulation of the S-matrix Bootstrap, at least once convergence is attained from both perspectives. These techniques are then applied to the study of a gapped system with two stable particles of different masses, which serves as a toy model for bootstrapping popular physical systems.

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.

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 Dual Approach to Recursive Optimization: Theory and Examples

Econometrica ◽  
2018 ◽  
Vol 86 (1) ◽  
pp. 133-172 ◽  
Author(s):  
Nicola Pavoni ◽  
Christopher Sleet ◽  
Matthias Messner
Keyword(s):  
Optimization Theory ◽  
Dual Approach ◽  
Recursive Optimization

A new variational expression for the scattering matrix

1988 ◽  
Vol 53 (9) ◽  
pp. 1873-1880 ◽  
Author(s):  
William H. Miller
Keyword(s):  
Variational Method ◽  
Scattering Matrix ◽  
Matrix Version ◽  
S Matrix ◽  
Concise Expression ◽  
Variational Expression

The S-matrix version of the Kohn variational method is used to obtain a new, more concise expression for the scattering matrix, one that has both esthetic and practical advantages over earlier ones that have been used.

Chern–Simons theories with fundamental matter: A brief review of large N results including Fermi–Bose duality and the S-matrix

2016 ◽  
Vol 31 (32) ◽  
pp. 1630052 ◽  
Author(s):  
Spenta R. Wadia
Keyword(s):  
String Theory ◽  
Gauge Fields ◽  
Duality Symmetry ◽  
Large N ◽  
Fundamental Matter ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Symmetry Relations ◽  
Aharonov Bohm ◽  
Chern Simons

We begin with a few words about Salam’s contribution to the growth of String Theory in India. In the technical talk we review results in [Formula: see text] Chern–Simons plus vector matter theories in 2[Formula: see text]+[Formula: see text]1 dim in the large [Formula: see text] limit. The dressing of charged matter by Chern–Simons gauge fields leads to anyons that interpolate between fermions and bosons and lead to a duality symmetry between fermionic and bosonic theories. The S-matrix (defined in the large [Formula: see text] limit) besides exhibiting this duality, also exhibits novel properties due to the presence of anyons. The S-matrix is not analytic, like in Aharonov–Bohm scattering, and satisfies modified crossing symmetry relations.

Unified S-matrix analysis of Airy structures in α+24Mg elastic and inelastic scattering

2018 ◽  
Vol 27 (07) ◽  
pp. 1850061 ◽  
Author(s):  
Yu. A. Berezhnoy ◽  
A. S. Molev ◽  
G. M. Onyshchenko ◽  
V. V. Pilipenko
Keyword(s):  
Inelastic Scattering ◽  
Cross Sections ◽  
Scattering Matrix ◽  
Matrix Analysis ◽  
Projectile Energy ◽  
Correct Description ◽  
First Order ◽  
Elastic And Inelastic Scattering ◽  
S Matrix ◽  
Nuclear Rainbow

Using the six-parameter [Formula: see text]-matrix model, we have obtained a simultaneous correct description of the [Formula: see text]Mg elastic and inelastic scattering differential cross-sections over the energy region [Formula: see text]–[Formula: see text] MeV, where typical nuclear rainbow and prerainbow patterns are observed. The Airy minima of the first-order have been unambiguously identified in the cross-sections for elastic scattering and inelastic scattering to the first 2[Formula: see text] state of [Formula: see text]Mg at [Formula: see text]–145[Formula: see text]MeV. Their angular positions obey an inverse dependence on energy, which is in line with the “rainbow” interpretation of the data. Within this interpretation, the scattering matrix and the deflection function for the system [Formula: see text]Mg at [Formula: see text]–240[Formula: see text]MeV show physically justified smooth variations with the projectile energy.

Dynamic Form of Static Dispersion Relations and Projective Spaces

1997 ◽  
Vol 12 (01) ◽  
pp. 249-254 ◽  
Author(s):  
V. A. Meshcheryakov
Keyword(s):  
Dispersion Relation ◽  
Global Analysis ◽  
Projective Spaces ◽  
Analytical Continuation ◽  
Physical Sheet ◽  
System Of Difference Equations ◽  
Static Limit ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Dynamic Form

The S-matrix in the static limit of a dispersion relation has a finite order N and is a matrix of meromorfic functions of energy ω in the plane with cuts (-∞, -1],[+1, = ∞). In the elastic case it reduces to N functions Si(ω) conncted by the crossing symmetry matrix A. The problem of analytical continuation of Si(ω) from the physical sheet to unphysical ones can be treated as a nonlinear system of difference equations. It is shown that a global analysis of this system can be carried out effectively in projective spaces PN and PN+1. The connection between spasec PN and PN+1 is discussed.

INTEGRALS OF MOTION IN SCALING 3-STATE POTTS MODEL FIELD THEORY

1988 ◽  
Vol 03 (03) ◽  
pp. 743-750 ◽  
Author(s):  
A.B. ZAMOLODCHIKOV
Keyword(s):  
Field Theory ◽  
Potts Model ◽  
Scattering Matrix ◽  
Integrals Of Motion ◽  
Model Field ◽  
S Matrix

Some nontrivial integrals of motion for the scaling 3-state Potts model are constructed explicitly. These integrals of motion prove the corresponding scattering matrix to be factorizable and allow one to “derive” this S-matrix under a few natural assumptions.

scholarly journals ON THE S MATRIX OF THE SUBLEADING MAGNETIC DEFORMATION OF THE TRICRITICAL ISING MODEL IN TWO DIMENSIONS

1992 ◽  
Vol 07 (21) ◽  
pp. 5281-5305 ◽  
Author(s):  
F. COLOMO ◽  
G. MUSSARDO ◽  
A. KOUBEK
Keyword(s):  
Ising Model ◽  
Finite Size ◽  
Numerical Data ◽  
Two Dimensions ◽  
Conformal Space ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Space Approach ◽  
Good Agreement

We compute the S matrix of the tricritical Ising model perturbed by the subleading magnetic operator using Smirnov’s RSOS reduction of the Izergin-Korepin model. The massive model contains kink excitations which interpolate between two degenerate asymmetric vacua. As a consequence of the different structure of the two vacua, the crossing symmetry is implemented in a nontrivial way. We use finite-size techniques to compare our results with the numerical data obtained by the truncated conformal space approach and find good agreement.

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