Related papers: Braid analysis of (low-dimensional) chaos
In this article, we give a numerical algorithm to compute braid groups of curves, hyperplane arrangements, and parameterized system of polynomial equations. Our main result is an algorithm that determines the cross-locus and the generators…
We study the degree of polynomial representations of knots. We obtain the lexicographic degree for two-bridge torus knots and generalized twist knots. The proof uses the braid theoretical method developed by Orevkov to study real plane…
We review the q-deformed spin network approact to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. These methods produce a concise proof…
This is an expository article on diagrammatic representations of knots and links in various settings via braids.
We consider mechanically generated molecular braids composed of two molecules where long range interactions between them can be considered to be very weak. We describe a model that takes account of the thermal fluctuations of the braid,…
We reduce complex stripped patterns to a basic topological network of edges and vertices to define defects and measure their influence on the pattern. We present statistics on the spatial and temporal distribution of defects within the…
In the work we discuss two invariants of conjugacy classes of braids. The first invariant is the conformal module which occurred in connection with the interest in the 13th Hilbert Problem. The second is a popular dynamical invariant, the…
While it is well known that three dimensional quantum many-body systems can support non-trivial braiding statistics between particle-like and loop-like excitations, or between two loop-like excitations, we argue that a more fundamental…
In this survey paper we present the $L$--moves between braids and how they can adapt and serve for establishing and proving braid equivalence theorems for various diagrammatic settings, such as for classical knots, for knots in knot…
Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…
We consider universal statistical properties of systems that are characterized by phase states with macroscopic degeneracy of the ground state. A possible topological order in such systems is described by non-linear discrete equations. We…
No systematic procedure currently exists for inferring the underlying physics from discrepancies observed in high energy collider data. We present Bard, an algorithm designed to facilitate the process of model construction at the energy…
Braiding matrices in rational conformal field theory are considered. The braiding matrices for any two block four point function are computed, in general, using the holomorphic properties of the blocks and the holomorphic properties of…
A simple and elegant arrangement of stock components of a portfolio (market index-DJIA) in a recent paper [1], has led to the construction of crossing of stocks diagram. The crossing stocks method revealed hidden remarkable algebraic and…
In this thesis, we present a comprehensive study of chaos and thermalization of the one-dimensional Bose-Hubbard Model (BHM) within the classical field approximation. Two quantitative measures are compared: the ensemble-averaged Finite-time…
The braiding operations of quantum states have attracted substantial attention due to their great potential for realizing topological quantum computations. In this paper, we show that a three-fold degenerate eigen subspace can be obtained…
Given a system of equations in a "random" finitely generated subgroup of the braid group, we show how to find a small ordered list of elements in the subgroup, which contains a solution to the equations with a significant probability.…
A special class of braids, called woven, is introduced and it is shown that every conjugation class of the braid group contains woven braids. In consequence, links can be presented as plats or closures of woven braids. Restricting on knots,…
The particle-scale dynamics of granular materials have commonly been characterized by the self-diffusion coefficient $D$. However, this measure discards the collective and topological information known to be an important characteristic of…
The recent suggestion that the entropy of Schwarzschild black holes can be computed in matrix theory using near-extremal D-brane thermodynamics is examined. It is found that the regime in which this approach is valid actually describes…