scholarly journals Universal entanglement signatures of foliated fracton phases

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Wilbur Shirley ◽  
Kevin Slagle ◽  
Xie Chen
Keyword(s):  
Fixed Point ◽  
Entanglement Entropy ◽  
Three Dimensional ◽  
Topological Phases ◽  
Topological Order ◽  
Two Dimensional ◽  
Adiabatic Evolution ◽  
Universal Properties ◽  
Three Dimensional Models ◽  
Topological Entanglement Entropy

Fracton models exhibit a variety of exotic properties and lie beyond the conventional framework of gapped topological order. In , we generalized the notion of gapped phase to one of foliated fracton phase by allowing the addition of layers of gapped two-dimensional resources in the adiabatic evolution between gapped three-dimensional models. Moreover, we showed that the X-cube model is a fixed point of one such phase. In this paper, according to this definition, we look for universal properties of such phases which remain invariant throughout the entire phase. We propose multi-partite entanglement quantities, generalizing the proposal of topological entanglement entropy designed for conventional topological phases. We present arguments for the universality of these quantities and show that they attain non-zero constant value in non-trivial foliated fracton phases.

scholarly journals Topological pseudo entropy

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Tatsuma Nishioka ◽  
Tadashi Takayanagi ◽  
Yusuke Taki
Keyword(s):  
Entanglement Entropy ◽  
Three Dimensional ◽  
Partition Functions ◽  
Two Dimensional ◽  
Arbitrary Boundary ◽  
Conformal Field ◽  
Boundary States ◽  
Dimensional Boundary ◽  
Topological Entanglement Entropy ◽  
Chern Simons

Abstract We introduce a pseudo entropy extension of topological entanglement entropy called topological pseudo entropy. Various examples of the topological pseudo entropies are examined in three-dimensional Chern-Simons gauge theory with Wilson loop insertions. Partition functions with knotted Wilson loops are directly related to topological pseudo (Rényi) entropies. We also show that the pseudo entropy in a certain setup is equivalent to the interface entropy in two-dimensional conformal field theories (CFTs), and leverage the equivalence to calculate the pseudo entropies in particular examples. Furthermore, we define a pseudo entropy extension of the left-right entanglement entropy in two-dimensional boundary CFTs and derive a universal formula for a pair of arbitrary boundary states. As a byproduct, we find that the topological interface entropy for rational CFTs has a contribution identical to the topological entanglement entropy on a torus.

Sight distance red zones on combined horizontal and sag vertical curves

1998 ◽  
Vol 25 (4) ◽  
pp. 621-630 ◽  
Author(s):  
Yasser Hassan ◽  
Said M Easa
Keyword(s):  
Quantitative Analysis ◽  
Three Dimensional ◽  
The Other ◽  
Two Dimensional ◽  
Horizontal Curve ◽  
Sight Distance ◽  
Stopping Sight Distance ◽  
Three Dimensional Models ◽  
Highway Alignment ◽  
Current Standards

Coordination of highway horizontal and vertical alignments is based on subjective guidelines in current standards. This paper presents a quantitative analysis of coordinating horizontal and sag vertical curves that are designed using two-dimensional standards. The locations where a horizontal curve should not be positioned relative to a sag vertical curve (called red zones) are identified. In the red zone, the available sight distance (computed using three-dimensional models) is less than the required sight distance. Two types of red zones, based on stopping sight distance (SSD) and preview sight distance (PVSD), are examined. The SSD red zone corresponds to the locations where an overlap between a horizontal curve and a sag vertical curve should be avoided because the three-dimensional sight distance will be less than the required SSD. The PVSD red zone corresponds to the locations where a horizontal curve should not start because drivers will not be able to perceive it and safely react to it. The SSD red zones exist for practical highway alignment parameters, and therefore designers should check the alignments for potential SSD red zones. The range of SSD red zones was found to depend on the different alignment parameters, especially the superelevation rate. On the other hand, the results showed that the PVSD red zones exist only for large values of the required PVSD, and therefore this type of red zones is not critical. This paper should be of particular interest to the highway designers and professionals concerned with highway safety.Key words: sight distance, red zone, combined alignment.

scholarly journals TSUNAMI GENERATION AND PROPAGATION

1972 ◽  
Vol 1 (13) ◽  
pp. 146
Author(s):  
Joseph L. Hammack ◽  
Frederic Raichlen
Keyword(s):  
Linear Theory ◽  
Source Region ◽  
Three Dimensional ◽  
Frequency Dispersion ◽  
Nonlinear Effects ◽  
Its Region ◽  
Experimental Results ◽  
Specific Class ◽  
Two Dimensional ◽  
Three Dimensional Models

A linear theory is presented for waves generated by an arbitrary bed deformation {in space and time) for a two-dimensional and a three -dimensional fluid domain of uniform depth. The resulting wave profile near the source is computed for both the two and three-dimensional models for a specific class of bed deformations; experimental results are presented for the two-dimensional model. The growth of nonlinear effects during wave propagation in an ocean of uniform depth and the corresponding limitations of the linear theory are investigated. A strategy is presented for determining wave behavior at large distances from the source where linear and nonlinear effects are of equal magnitude. The strategy is based on a matching technique which employs the linear theory in its region of applicability and an equation similar to that of Korteweg and deVries (KdV) in the region where nonlinearities are equal in magnitude to frequency dispersion. Comparison of the theoretical computations with the experimental results indicates that an equation of the KdV type is the proper model of wave behavior at large distances from the source region.

scholarly journals Boundary Topological Entanglement Entropy in Two and Three Dimensions

2021 ◽  
Author(s):  
Jacob C. Bridgeman ◽  
Benjamin J. Brown ◽  
Samuel J. Elman
Keyword(s):  
General Property ◽  
Entanglement Entropy ◽  
Quantum Correlations ◽  
Three Dimensions ◽  
Topological Phases ◽  
Fusion Categories ◽  
Special Cases ◽  
Constructive Proofs ◽  
And Algebra ◽  
Topological Entanglement Entropy

AbstractThe topological entanglement entropy is used to measure long-range quantum correlations in the ground space of topological phases. Here we obtain closed form expressions for the topological entropy of (2+1)- and (3+1)-dimensional loop gas models, both in the bulk and at their boundaries, in terms of the data of their input fusion categories and algebra objects. Central to the formulation of our results are generalized $${\mathcal {S}}$$ S -matrices. We conjecture a general property of these $${\mathcal {S}}$$ S -matrices, with proofs provided in many special cases. This includes constructive proofs for categories up to rank 5.

scholarly journals On the Measure-Preserving Mappings with Three-Dimensions

1993 ◽  
Vol 132 ◽  
pp. 73-89
Author(s):  
Yi-Sui Sun
Keyword(s):  
Fixed Point ◽  
Invariant Manifolds ◽  
Three Dimensional ◽  
Invariant Curve ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Kolmogorov Entropy ◽  
Numerical Exploration ◽  
Area Preserving ◽  
Dimensional Mapping

AbstractWe have systematically made the numerical exploration about the perturbation extension of area-preserving mappings to three-dimensional ones, in which the fixed points of area preserving are elliptic, parabolic or hyperbolic respectively. It has been observed that: (i) the invariant manifolds in the vicinity of the fixed point generally don’t exist (ii) when the invariant curve of original two-dimensional mapping exists the invariant tubes do also in the neighbourhood of the invariant curve (iii) for the perturbation extension of area-preserving mapping the invariant manifolds can only be generated in the subset of the invariant manifolds of original two-dimensional mapping, (iv) for the perturbation extension of area preserving mappings with hyperbolic or parabolic fixed point the ordered region near and far from the invariant curve will be destroyed by perturbation more easily than the other one, This is a result different from the case with the elliptic fixed point. In the latter the ordered region near invariant curve is solid. Some of the results have been demonstrated exactly.Finally we have discussed the Kolmogorov Entropy of the mappings and studied some applications.

scholarly journals The Algorithm for Determining the Coordinates of a Point in Three-Dimensional Space by Using the Auxiliary Point

2013 ◽  
Vol 48 (4) ◽  
pp. 141-145 ◽  
Author(s):  
Bartlomiej Oszczak ◽  
Eliza Sitnik
Keyword(s):  
Fixed Point ◽  
Precise Measurement ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Satellite Navigation ◽  
Reference Points ◽  
Two Dimensional ◽  
Approximate Location ◽  
The Many ◽  
Three Dimensional Space

ABSTRACT During the process of satellite navigation, and also in the many tasks of classical positioning, we need to calculate the corrections to the initial (or approximate) location of the point using precise measurement of distances to the permanent points of reference (reference points). In this paper the authors have provided a way of developing Hausbrandt's equations, on the basis of which the exact coordinates of the point in two-dimensional space can be determined by using the computed correction to the coordinates of the auxiliary point. The authors developed generalised equations for threedimensional space introducing additional fixed point and have presented proof of derived formulas.

Three-Dimensional Mesh Model Watermarking Algorithm

2012 ◽  
Vol 198-199 ◽  
pp. 1481-1486
Author(s):  
Xin Li ◽  
Yi Ping Tian
Keyword(s):  
Wavelet Transform ◽  
Copyright Protection ◽  
Control Point ◽  
Three Dimensional ◽  
Digital Watermark ◽  
Two Dimensional ◽  
Mesh Model ◽  
Watermark Embedding ◽  
Three Dimensional Models ◽  
Watermark Algorithm

Watermark information is embedded in three-dimensional mesh model through three-dimensional watermarking algorithm for effective copyright protection. The widely use of three-dimensional grid model attracts more attention on the copyright protection. The digital watermark algorithm with the NURBS model based on the wavelet transform aims to get the virtual grayscale images using the control point coordinate. Then we can embed the watermark into the virtual gray image watermark. It can change the three-dimensional models into two-dimensional images. And this algorithm can enhance the operability and simplicity of the watermark embedding. Experiments show that the proposed algorithm is easy to implement, simple in principle, and the extracted watermark is clearly visible, moreover, the model does not need to be directly modified, so it has good robustness. Watermarked model does not change in the visual, it has good invisibility.

Two-Dimensional R-Matrices — Descendants of Three-Dimensional R-Matrices

1997 ◽  
Vol 12 (19) ◽  
pp. 1393-1410 ◽  
Author(s):  
S. M. Sergeev
Keyword(s):  
Three Dimensional ◽  
Baxter Equation ◽  
Two Dimensional ◽  
Affine Algebra ◽  
Tetrahedron Equation ◽  
Drinfeld Double ◽  
R Matrix ◽  
Operator Solution ◽  
Dimensional Models ◽  
Three Dimensional Models

Finite layers of three-dimensional models can be regarded as two-dimensional with complicated multi-stated weights. The tetrahedron equation in 3D provides the Yang–Baxter equation for this composite weights in 2D. Such solutions of the Yang–Baxter equation are constructed for the simplest operator solution of the tetrahedron equation. These R-matrices can be regarded as a special projection of universal R-matrix for some Drinfeld double [Formula: see text], associated with the affine algebra [Formula: see text]. Usual R-matrix for [Formula: see text] is another projection of [Formula: see text].

Sign in / Sign up

Export Citation Format

Share Document