scholarly journals Particles, conformal invariance and criticality in pure and disordered systems

2021 ◽  
Vol 94 (3) ◽  
Author(s):  
Gesualdo Delfino
Keyword(s):  
Conformal Invariance ◽  
Disordered Systems ◽  
Short Range ◽  
Recent Progress ◽  
Quenched Disorder ◽  
Exact Methods ◽  
Special Position ◽  
Infinite Dimensional ◽  
First Order ◽  
The Continuum

AbstractThe two-dimensional case occupies a special position in the theory of critical phenomena due to the exact results provided by lattice solutions and, directly in the continuum, by the infinite-dimensional character of the conformal algebra. However, some sectors of the theory, and most notably criticality in systems with quenched disorder and short-range interactions, have appeared out of reach of exact methods and lacked the insight coming from analytical solutions. In this article, we review recent progress achieved implementing conformal invariance within the particle description of field theory. The formalism yields exact unitarity equations whose solutions classify critical points with a given symmetry. It provides new insight in the case of pure systems, as well as the first exact access to criticality in presence of short range quenched disorder. Analytical mechanisms emerge that in the random case allow the superuniversality of some critical exponents and make explicit the softening of first-order transitions by disorder.Graphic abstract

Unification of Gauge Forces and Gravity using Tangled Vortex Knots and Entanglement Dynamics

2020 ◽  
Author(s):  
Mrittunjoy Guha Majumdar
Keyword(s):  
Field Theory ◽  
Short Range ◽  
Gauge Fields ◽  
Entanglement Dynamics ◽  
Unified Field Theory ◽  
Linear Dynamics ◽  
Unified Field ◽  
The Standard Model ◽  
Theory Of Everything ◽  
The Continuum

In this paper, the statistics of excitation-tangles in a postulated background ideal-superfluid field is studied. The structure of the Standard Model is derived in terms of tangle vortex-knots and soliton. Gravity is observed in terms of torsion and curvature in the continuum. In this way, non-linear dynamics and excitations give rise to a unified field theory as well as a Theory of Everything. As a result of this unification, spacetime and matter are shown to be fundamentally equivalent, while gauge fields arise from reorientation and excitations of the the fundamental underlying field. Finally, the equivalence of topological and quantum entanglement is explored to posit a theory of everything in terms of long- and short-range entanglement between fundamental quantum units (bits) of information.

Pattern Theory

2006 ◽  
Author(s):  
Ulf Grenander ◽  
Michael I. Miller
Keyword(s):  
Computational Linguistics ◽  
Parametric Representation ◽  
Bayes Estimation ◽  
Geometric Transformation ◽  
Central Component ◽  
Pattern Theory ◽  
Infinite Dimensional ◽  
Engineering Mathematics ◽  
Dimensional Shape ◽  
The Continuum

Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science, and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website. The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.

scholarly journals Glassy behaviour in short-range lattice models without quenched disorder

2002 ◽  
Vol 82 (5) ◽  
pp. 617-623 ◽  
Author(s):  
Mário J. de Oliveira ◽  
Alberto Petri
Keyword(s):  
Short Range ◽  
Lattice Models ◽  
Quenched Disorder

scholarly journals The X-Ray Nova GRO J0422+32 in Decline and Quiescence

1996 ◽  
Vol 158 ◽  
pp. 399-400
Author(s):  
M. R. Garcia ◽  
P. J. Callanan ◽  
J. E. McClintock ◽  
P. Zhao
Keyword(s):  
Emission Line ◽  
Emission Region ◽  
Dwarf Novae ◽  
X Ray ◽  
First Order ◽  
Band Emission ◽  
Line Region ◽  
Hα Emission ◽  
The Stability ◽  
The Continuum

We have followed the X-ray nova GRO J0422+32, spectroscopically and photometrically, throughout the decline to quiescence.In the final stages of decay (days 430…880 after the outburst, see Callanan et al. (1995) for the epoch 1995), the equivalent width (EW) of the Hα emission increases monotonically and the R magnitude decreases monotonically. This suggests that the flux in the Hα line is constant, while the continuum fades. The Hα flux is the product of the R band flux (F(R), arbitrarily scaled to 100 at R = 19 mag) and the EW, and is shown in the last column of the table below. The Hα flux varies by only ~ 30% while the continuum fades by a factor of eight (from R = 19 mag to R = 21.3 mag). So, to first order, the Hα luminosity is constant in the final stages of decay. While it is generally the case that the emission line EWs in individual dwarf novae also increase during the decay, the exact behavior seen in GRO J0422+32 is not what is seen for dwarf novae (on average). Using the relation between EW[Hβ] and Mv given in figure 6 of Patterson (1984), we would expect a factor of ~ 5 variation in the Hα flux during days 430…880. The stability of the Hα flux implies that somehow the emission line region is ‘disconnected’ from the continuum (R–band) emission region.

scholarly journals Integral operators, bispectrality and growth of Fourier algebras

2020 ◽  
Vol 2020 (766) ◽  
pp. 151-194 ◽  
Author(s):  
W. Riley Casper ◽  
Milen T. Yakimov
Keyword(s):  
Differential Operator ◽  
Integral Kernel ◽  
Exact Estimate ◽  
Airy Functions ◽  
Direct Computation ◽  
Infinite Dimensional ◽  
First Order ◽  
Rank 2 ◽  
Commuting Differential Operator ◽  
Algorithmic Procedure

AbstractIn the mid 1980s it was conjectured that every bispectral meromorphic function {\psi(x,y)} gives rise to an integral operator {K_{\psi}(x,y)} which possesses a commuting differential operator. This has been verified by a direct computation for several families of functions {\psi(x,y)} where the commuting differential operator is of order {\leq 6}. We prove a general version of this conjecture for all self-adjoint bispectral functions of rank 1 and all self-adjoint bispectral Darboux transformations of the rank 2 Bessel and Airy functions. The method is based on a theorem giving an exact estimate of the second- and first-order terms of the growth of the Fourier algebra of each such bispectral function. From it we obtain a sharp upper bound on the order of the commuting differential operator for the integral kernel {K_{\psi}(x,y)} leading to a fast algorithmic procedure for constructing the differential operator; unlike the previous examples its order is arbitrarily high. We prove that the above classes of bispectral functions are parametrized by infinite-dimensional Grassmannians which are the Lagrangian loci of the Wilson adelic Grassmannian and its analogs in rank 2.

scholarly journals Viscous fingering in the presence of weak disorder

2020 ◽  
Vol 15 ◽  
pp. 2
Author(s):  
Eldad Bettelheim ◽  
Oded Agam
Keyword(s):  
Correlation Function ◽  
Fractal Dimension ◽  
Harmonic Measure ◽  
Short Range ◽  
Viscous Fingering ◽  
Quenched Disorder ◽  
Weak Disorder ◽  
Box Counting ◽  
Point Correlation ◽  
Point Correlation Function

We consider the problem of viscous fingering in the presence of quenched disorder, that is both weak and short-range correlated. The two-point correlation function of the harmonic measure is calculated perturbatively, and is used in order to calculate the correction and the box-counting fractal dimension. We show that the disorder increases the fractal dimension, and that its effect decreases logarithmically with the size of the fractal.

scholarly journals First-order discrete Faddeev gravity at strongly varying fields

2017 ◽  
Vol 32 (35) ◽  
pp. 1750181
Author(s):  
V. M. Khatsymovsky
Keyword(s):  
Dimensional Space ◽  
Tetrad Field ◽  
First Order ◽  
Antiferromagnetic Structure ◽  
Riemannian Connection ◽  
Order Representation ◽  
Independent Variable ◽  
The Continuum ◽  
Elementary Area ◽  
Classical Background

We consider the Faddeev formulation of general relativity (GR), which can be characterized by a kind of d-dimensional tetrad (typically d = 10) and a non-Riemannian connection. This theory is invariant w.r.t. the global, but not local, rotations in the d-dimensional space. There can be configurations with a smooth or flat metric, but with the tetrad that changes abruptly at small distances, a kind of “antiferromagnetic” structure. Previously, we discussed a first-order representation for the Faddeev gravity, which uses the orthogonal connection in the d-dimensional space as an independent variable. Using the discrete form of this formulation, we considered the spectrum of (elementary) area. This spectrum turns out to be physically reasonable just on a classical background with large connection like rotations by [Formula: see text], that is, with such an “antiferromagnetic” structure. In the discrete first-order Faddeev gravity, we consider such a structure with periodic cells and large connection and strongly changing tetrad field inside the cell. We show that this system in the continuum limit reduces to a generalization of the Faddeev system. The action is a sum of related actions of the Faddeev type and is still reduced to the GR action.

Sign in / Sign up

Export Citation Format

Share Document