S-matrix Theory

2020 ◽  
pp. 622-675
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Matrix Theory ◽  
Point Of View ◽  
Integrable Models ◽  
Geometrical Interpretation ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Recursive Structure ◽  
Mathematical Point ◽  
S Matrix ◽  
Dynamical Principle

Chapter 17 discusses the S-matrix theory of two-dimensional integrable models. From a mathematical point of view, the two-dimensional nature of the systems and their integrability are the crucial features that lead to important simplifications of the formalism and its successful application. This chapter deals with the analytic theory of the S-matrix of the integrable models. A particular emphasis is put on the dynamical principle of bootstrap, which gives rise to a recursive structure of the amplitudes. It also covers several dynamical quantities, such as mass ratios or three-coupling constants, which have an elegant mathematic formulation that is also of easy geometrical interpretation.

scholarly journals Two-dimensional Scattering by a Potential without a Classical Analogue

1999 ◽  
Vol 52 (5) ◽  
pp. 859 ◽  
Author(s):  
I. V. Ponomarev
Keyword(s):  
Quantum Chaos ◽  
Matrix Theory ◽  
Delta Function ◽  
Two Dimensional ◽  
Dirac Delta ◽  
S Matrix ◽  
Classical Analogue ◽  
Scattering Potential ◽  
The One ◽  
The Given

A two-dimensional scattering potential represents the quantum extension of a diffractive lattice: a Dirac delta function with a modulated permeability along the y-axis. This model does not have an explicit classical analogue and quantum effects such as tunneling and diffraction play an important role. An analytical solution for the one-harmonic case is found. For the general case of an arbitrary number of harmonics a simple criterion is derived for the range of parameters where quantum chaos is permitted (but does not necessarily occur). The statistical properties of the S-matrix for the given model have been investigated. The deviations from the usual predictions for irregular scattering in the random matrix theory (RMT) framework have been found and are discussed.

scholarly journals Contact interactions in complex fibrous metamaterials

2021 ◽  
Author(s):  
Mario Spagnuolo ◽  
Antonio M. Cazzani
Keyword(s):  
Strain Energy ◽  
Point Of View ◽  
The Other ◽  
Contact Interactions ◽  
Coupling Term ◽  
Dissipation Potential ◽  
Parallel Fibers ◽  
Mathematical Point

AbstractIn this work, an extension of the strain energy for fibrous metamaterials composed of two families of parallel fibers lying on parallel planes and joined by connective elements is proposed. The suggested extension concerns the possibility that the constituent fibers come into contact and eventually scroll one with respect to the other with consequent dissipation due to friction. The fibers interact with each other in at least three different ways: indirectly, through microstructural connections that could allow a relative sliding between the two families of fibers; directly, as the fibers of a family can touch each other and can scroll introducing dissipation. From a mathematical point of view, these effects are modeled first by introducing two placement fields for the two fiber families and adding a coupling term to the strain energy and secondly by adding two other terms that take into account the interdistance between the parallel fibers and the Rayleigh dissipation potential (to account for friction).

A STUDY OF TWO‐DIMENSIONAL HEAD WAVES IN FLUID AND SOLID SYSTEMS

Geophysics ◽  
1963 ◽  
Vol 28 (4) ◽  
pp. 563-581 ◽  
Author(s):  
John W. Dunkin
Keyword(s):  
Half Space ◽  
Vertical Displacement ◽  
Point Of View ◽  
Head Wave ◽  
Apparent Velocity ◽  
Two Dimensional ◽  
Multiple Reflections ◽  
Transient Wave ◽  
Line Load ◽  
Head Waves

The problem of transient wave propagation in a three‐layered, fluid or solid half‐plane is investigated with the point of view of determining the effect of refracting bed thickness on the character of the two‐dimensional head wave. The “ray‐theory” technique is used to obtain exact expressions for the vertical displacement at the surface caused by an impulsive line load. The impulsive solutions are convolved with a time function having the shape of one cycle of a sinusoid. The multiple reflections in the refracting bed are found to affect the head wave significantly. For thin refracting beds in the fluid half‐space the character of the head wave can be completely altered by the strong multiple reflections. In the solid half‐space the weaker multiple reflections affect both the rate of decay of the amplitude of the head wave with distance and the apparent velocity of the head wave by changing its shape. A comparison is made of the results for the solid half‐space with previously published results of model experiments.

IMBEDDING OF TRANSFORMATION GROUPS IN AFFINE ONES AND RENORMALIZATION OF TWO-DIMENSIONAL HOMOGENEOUS σ-MODELS

1993 ◽  
Vol 08 (31) ◽  
pp. 2937-2942
Author(s):  
A. V. BRATCHIKOV
Keyword(s):  
Homogeneous Space ◽  
Transformation Group ◽  
Affine Group ◽  
Coupling Constants ◽  
Transformation Groups ◽  
Two Dimensional

The BLZ method for the analysis of renormalizability of the O(N)/O(N − 1) model is extended to the σ-model built on an arbitrary homogeneous space G/H and in arbitrary coordinates. For deriving Ward-Takahashi (WT) identities an imbedding of the transformation group G in an affine group is used. The structure of the renormalized action is found. All the infinities can be absorbed in a coupling constants renormalization and in a renormalization of auxiliary constants which are related to the imbedding.

Poly[[μ2-1,3-bis(pyridin-4-yl)propane](μ3-1,4-phenylenediacetato)cadmium]

2012 ◽  
Vol 68 (2) ◽  
pp. m34-m36 ◽  
Author(s):  
Dong Liu
Keyword(s):  
Title Complex ◽  
Point Of View ◽  
Solvothermal Reaction ◽  
Dimensional Chain ◽  
Two Dimensional ◽  
One Dimensional ◽  
Connected Network ◽  
Dimensional Network

Solvothermal reaction between Cd(NO3)2, 1,4-phenylenediacetate (1,4-PDA) and 1,3-bis(pyridin-4-yl)propane (bpp) afforded the title complex, [Cd(C10H8O4)(C13H14N2)]n. Adjacent carboxylate-bridged CdIIions are related by an inversion centre. The 1,4-PDA ligands adopt acisconformation and connect the CdIIions to form a one-dimensional chain extending along thecaxis. These chains are in turn linked into a two-dimensional network through bpp bridges. The bpp ligands adopt ananti–gaucheconformation. From a topological point of view, each bpp ligand and each pair of 1,4-PDA ligands can be considered as linkers, while the dinuclear CdIIunit can be regarded as a 6-connecting node. Thus, the structure can be simplified to a two-dimensional 6-connected network.

Structural studies of digitoxin and related cardenolides by two-dimensional NMR

1990 ◽  
Vol 68 (2) ◽  
pp. 272-277 ◽  
Author(s):  
Torbjörn Drakenberg ◽  
Peter Brodelius ◽  
Deane D. McIntyre ◽  
Hans J Vogel
Keyword(s):  
Nmr Spectroscopy ◽  
Nmr Spectra ◽  
Chair Conformation ◽  
Coupling Constants ◽  
Two Dimensional ◽  
Structural Studies ◽  
Solution Conformation ◽  
Phase Sensitive ◽  
Multiple Relay ◽  
C Nmr

The 1H and 13C NMR spectra of the cardenolides digitoxigenin, digoxigenin, digitoxin, and mono- and bis-digitoxigenin digitoxosides have been completely assigned by two-dimensional NMR spectroscopy. The techniques used include phase-sensitive COSY, multiple relay COSY, and carbon–proton correlation (HETCOR and HMQC) spectra. Various aspects of the solution conformation of the steroid moiety of digitoxin and digoxigenin could be determined from coupling constants and NOE difference experiments and they are indicative of an all-chair conformation. The carbohydrate rings in digitoxin and the mono- and bis-digitoxigenin digitoxosides are also in the chair conformation. Keywords: cardenolides, digitoxigenin, digitoxin, 2-dimensional NMR, conformational analysis.

scholarly journals INTEGRABLE HIERARCHIES AND CONTACT TERMS IN u-PLANE INTEGRALS OF TOPOLOGICALLY TWISTED SUPERSYMMETRIC GAUGE THEORIES

1999 ◽  
Vol 14 (07) ◽  
pp. 1001-1013 ◽  
Author(s):  
KANEHISA TAKASAKI
Keyword(s):  
Integrable Hierarchies ◽  
Gauge Theories ◽  
Point Of View ◽  
Coupling Constants ◽  
Integrable Hierarchy ◽  
Supersymmetric Gauge Theories ◽  
Tau Function ◽  
Single Time ◽  
Whitham Equations ◽  
Supersymmetric Gauge

The u-plane integrals of topologically twisted N=2 supersymmetric gauge theories generally contain contact terms of nonlocal topological observables. This paper proposes an interpretation of these contact terms from the point of view of integrable hierarchies and their Whitham deformations. This is inspired by Mariño and Moore's remark that the blowup formula of the u-plane integral contains a piece that can be interpreted as a single-time tau function of an integrable hierarchy. This single-time tau function can be extended to a multitime version without spoiling the modular invariance of the blowup formula. The multitime tau function is comprised of a Gaussian factor eQ(t1,t2,…) and a theta function. The time variables tn play the role of physical coupling constants of two-observables In(B) carried by the exceptional divisor B. The coefficients qmn of the Gaussian part are identified to be the contact terms of these two-observables. This identification is further examined in the language of Whitham equations. All relevant quantities are written in the form of derivatives of the prepotential.

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