Abelian string and particle braiding in topological order: Modular SL(3,Z) representation and (3 + 1)-dimensional twisted gauge theory." Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you...

We compute the braiding for the 'principal gradation' of U q (sl 2) for |q| = 1 from first principles, starting from the idea of a rigid braided tensor category. It is not necessary to assume either the crossing or the unitarity condition, from S-matrix theory. We demonstrate the uniqueness of the normalisation of the braiding under certain analyticity assumptions, and show that its convergence...

This thesis concerns applications of topology in magnetic fields. First, we examine the influence of writhe in the stretch-twist-fold dynamo. We consider a thin flux tube distorted by simple stretch, twist, and fold motions and calculate the helicity and energy spectra. The writhe number assists in the calculations, as it tells us how much the internal twist changes as the tube is distorted. In...

In this paper we study unitary braid group representations associated with Majorana Fermions. Majorana Fermions are represented by Majorana operators, elements of a Clifford algebra. The paper recalls and proves a general result about braid group representations associated with Clifford algebras, and compares this result with the Ivanov braiding associated with Majorana operators. The paper gen...

Majorana fermions are long-sought exotic particles that are their own antiparticles. Here we propose to utilize superconducting circuits to construct two superconducting-qubit arrays where Majorana modes can occur. A so-called Majorana qubit is encoded by using the unpaired Majorana modes, which emerge at the left and right ends of the chain in the Majorana-fermion representation. We also show ...

The unitary braiding operators describing topological entanglements can be viewed as universal quantum gates for quantum computation. With the help of the Brylinski’s theorem, the unitary solutions of the quantum Yang–Baxter equation can be also related to universal quantum gates. This paper derives unitary solutions of the quantum Yang–Baxter equation via Yang–Baxterization from the solutions ...