Clebsch-Gordan and 6j-coefficients for rank two quantum groups

We calculate (q-deformed) Clebsch-Gordan and 6j-coefficients for rank two quantum groups. We explain in detail how such calculations are done, which should allow the reader to perform similar calculations in other cases. Moreover, we tabulate the q-Clebsch-Gordan and 6j-coefficients explicitly, as well as some other topological data associated with theories corresponding to rank-two quantum groups. Finally, we collect some useful properties of the fusion rules of particular conformal field theories.Comment: 43 pages. v2: minor changes and added references. For mathematica notebooks containing the various q-CG and 6j symbols, see http://arxiv.org/src/1004.5456/an

Numerical simulation of non-Abelian anyons

Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a many-body system of non-interacting anyons. We introduce an algorithm that allows to simulate anyonic tight-binding Hamiltonians on two-dimensional lattices. The algorithm is directly derived from the low energy topological quantum field theory and is suited for general Abelian and non-Abelian anyon models. As concrete examples, we apply the algorithm to study the energy level spacing statistics, which reveals level repulsion for free semions, Fibonacci anyons, and Ising anyons. Additionally, we simulate nonequilibrium quench dynamics, where we observe that the density distribution becomes homogeneous for large times - indicating thermalization

Neoadjuvant chemoradiotherapy plus surgery versus active surveillance for oesophageal cancer: A stepped-wedge cluster randomised trial

Background: Neoadjuvant chemoradiotherapy (nCRT) plus surgery is a standard treatment for locally advanced oesophageal cancer. With this treatment, 29% of patients have a pathologically complete response in the resection specimen. This provides the rationale for investigating an active surveillance approach. The aim of this study is to assess the (cost-)effectiveness of active surveillance vs. standard oesophagectomy after nCRT for oesophageal cancer. Methods: This is a phase-III multi-centre, stepped-wedge cluster randomised controlled trial. A total of 300 patients with clinically complete response (cCR, i.e. no local or disseminated disease proven by histology) after nCRT will be randomised to show non-inferiority of active surveillance to standard oesophagectomy (non-inferiority margin 15%, intra-correlation coefficient 0.02, power 80%, 2-sided α 0.05, 12% drop-out). Patients will undergo a first clinical response evaluation (CRE-I) 4-6 weeks after nCRT, consisting of endoscopy with bite-on-bite biopsies of the primary tumour site and other suspected lesions. Clinically complete responders will undergo a second CRE (CRE-II), 6-8 weeks after CRE-I. CRE-II will include 18F-FDG-PET-CT, followed by endoscopy with bite-on-bite biopsies and ultra-endosonography plus fine needle aspiration of suspected lymph nodes and/or PET- positive lesions. Patients with cCR at CRE-II will be assigned to oesophagectomy (first phase) or active surveillance (second phase of the study). The duration of the first phase is determined randomly over the 12 centres, i.e., stepped-wedge cluster design. Patients in the active surveillance arm will undergo diagnostic evaluations similar to CRE-II at 6/9/12/16/20/24/30/36/48 and 60 months after nCRT. In this arm, oesophagectomy will be offered only to patients in whom locoregional regrowth is highly suspected or proven, without distant dissemination. The main study parameter is overall survival; secondary endpoints include percentage of patients who do not undergo surgery, quality of life, clinical irresectability (cT4b) rate, radical resection rate, postoperative complications, progression-free survival, distant dissemination rate, and cost-effectiveness. We hypothesise that active surveillance leads to non-inferior survival, improved quality of life and a reduction in costs, compared to standard oesophagectomy. Discussion: If active surveillance and surgery as needed after nCRT leads to non-inferior survival compared to standard oesophagectomy, this organ-sparing approach can be implemented as a standard of care

Compatibility of Braiding and Fusion on Wire Networks

Exchanging particles on graphs, or more concretely on networks of quantum wires, has been proposed as a means to perform fault tolerant quantum computation. This was inspired by braiding of anyons in planar systems. However, exchanges on a graph are not governed by the usual braid group but instead by a graph braid group. By imposing compatibility of graph braiding with fusion of topological charges, we obtain generalized hexagon equations. We find the usual planar anyons solutions but also more general braid actions. We illustrate this with Abelian, Fibonacci and Ising fusion rules.Comment: 7 pages, 4 figure