S-Matrices of ϕ1,2\phi_{1,2} perturbed unitary minimal models: IRF-Formulation and Bootstrap-Program

We analyze the algebraic structure of $\phi_{1,2}$ perturbed minimal models relating them to graph-state models with an underlying Birman-Wenzl-Murakami algebra. Using this approach one can clarify some physical properties and reformulate the bootstrap equations. These are used to calculate the $S$-matrix elements of higher kinks, and to determine the breather spectrum of the $\phi_{1,2}$ perturbations of the unitary minimal models \M_{r,r+1}.Comment: 20 pp, SISSA 192/92/E

Fast algorithms for min independent dominating set

We first devise a branching algorithm that computes a minimum independent dominating set on any graph with running time O*(2^0.424n) and polynomial space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs, Proc. WG'06). We then show that, for every r>3, it is possible to compute an r-((r-1)/r)log_2(r)-approximate solution for min independent dominating set within time O*(2^(nlog_2(r)/r))

Geometric Presentations of Braid Groups for Particles on a Graph

We study geometric presentations of braid groups for particles that are constrained to move on a graph, i.e. a network consisting of nodes and edges. Our proposed set of generators consists of exchanges of pairs of particles on junctions of the graph and of certain circular moves where one particle travels around a simple cycle of the graph. We point out that so defined generators often do not satisfy the braiding relation known from 2D physics. We accomplish a full description of relations between the generators for star graphs where we derive certain quasi-braiding relations. We also describe how graph braid groups depend on the (graph-theoretic) connectivity of the graph. This is done in terms of quotients of graph braid groups where one-particle moves are put to identity. In particular, we show that for $3$-connected planar graphs such a quotient reconstructs the well-known planar braid group. For $2$-connected graphs this approach leads to generalisations of the Yang-Baxter equation. Our results are of particular relevance for the study of non-abelian anyons on networks showing new possibilities for non-abelian quantum statistics on graphs

The abundance of 28Si32S, 29Si32S, 28Si34S, and 30Si32S in the inner layers of the envelope of IRC+10216

We present high spectral resolution mid-IR observations of SiS towards the C-rich AGB star IRC+10216 carried out with the Texas Echelon-cross-Echelle Spectrograph mounted on the NASA Infrared Telescope Facility. We have identified 204 ro-vibrational lines of 28Si32S, 26 of 29Si32S, 20 of 28Si34S, and 15 of 30Si32S in the frequency range 720-790 cm-1. These lines belong to bands v=1-0, 2-1, 3-2, 4-3, and 5-4, and involve rotational levels with Jlow<90. About 30 per cent of these lines are unblended or weakly blended and can be partially or entirely fitted with a code developed to model the mid-IR emission of a spherically symmetric circumstellar envelope composed of expanding gas and dust. The observed lines trace the envelope at distances to the star <35R* (~0.7 arcsec). The fits are compatible with an expansion velocity of 1+2.5(r/R*-1) km/s between 1 and 5R*, 11 km/s between 5 and 20R*, and 14.5 km/s outwards. The derived abundance profile of 28Si32S with respect to H2 is 4.9e-6 between the stellar photosphere and 5R*, decreasing linearly to 1.6e-6 at 20R* and to 1.3e-6 at 50R*. 28Si32S seems to be rotationally under LTE in the region of the envelope probed with our observations and vibrationally out of LTE in most of it. There is a red-shifted emission excess in the 28Si32S lines of band v=1-0 that cannot be found in the lines of bands v=2-1, 3-2, 4-3, and 5-4. This excess could be explained by an enhancement of the vibrational temperature around 20R* behind the star. The derived isotopic ratios 28Si/29Si, and 32S/34S are 17 and 14, compatible with previous estimates.Comment: 11 pages, 5 figures, and 4 tables. Accepted for publication in MNRA