Noncompact dynamical symmetry of a spin-orbit coupled oscillator

We explain the finite as well as infinite degeneracy in the spectrum of a particular system of spin-1/2 fermions with spin-orbit coupling in three spatial dimensions. Starting from a generalized Runge-Lenz vector, we explicitly construct a complete set of symmetry operators, which span a noncompact SO(3,2) algebra. The degeneracy of the physical spectrum only involves a particular, infinite, so called singleton representation. In the branch where orbital and spin angular momentum are aligned the full representation appears, constituting a 3D analogue of Landau levels. Anti-aligning the spin leads to a finite degeneracy due to a truncation of the singleton representation. We conclude the paper by constructing the spectrum generating algebra of the problem

Diagrammatics for Bose condensation in anyon theories

Phase transitions in anyon models in (2+1)-dimensions can be driven by condensation of bosonic particle sectors. We study such condensates in a diagrammatic language and explicitly establish the relation between the states in the fusion spaces of the theory with the condensate, to the states in the parent theory using a new set of mathematical quantities called vertex lifting coefficients (VLCs). These allow one to calculate the full set of topological data ($S$-, $T$-, $R$- and $F$-matrices) in the condensed phase. We provide closed form expressions of the topological data in terms of the VLCs and provide a method by which one can calculate the VLCs for a wide class of bosonic condensates. We furthermore furnish a concrete recipe to lift arbitrary diagrams directly from the condensed phase to the original phase, such that they can be evaluated using the data of the original theory and a limited number of VLCs. Some representative examples are worked out in detail.Comment: 20 pages, 1 figure, many diagram

The modular S-matrix as order parameter for topological phase transitions

We study topological phase transitions in discrete gauge theories in two spatial dimensions induced by the formation of a Bose condensate. We analyse a general class of euclidean lattice actions for these theories which contain one coupling constant for each conjugacy class of the gauge group. To probe the phase structure we use a complete set of open and closed anyonic string operators. The open strings allow one to determine the particle content of the condensate, whereas the closed strings enable us to determine the matrix elements of the modular $S$-matrix, also in the broken phase. From the measured broken $S$-matrix we may read off the sectors that split or get identified in the broken phase, as well as the sectors that are confined. In this sense the modular $S$-matrix can be employed as a matrix valued non-local order parameter from which the low-energy effective theories that occur in different regions of parameter space can be fully determined. To verify our predictions we studied a non-abelian anyon model based on the quaternion group $H=\bar{D_2}$ of order eight by Monte Carlo simulation. We probe part of the phase diagram for the pure gauge theory and find a variety of phases with magnetic condensates leading to various forms of (partial) confinement in complete agreement with the algebraic breaking analysis. Also the order of various transitions is established.Comment: 37 page

More on core instabilities of magnetic monopoles

In this paper we present new results on the core instability of the 't Hooft Polyakov monopoles we reported on before. This instability, where the spherical core decays in a toroidal one, typically occurs in models in which charge conjugation is gauged. In this paper we also discuss a third conceivable configuration denoted as ``split core'', which brings us to some details of the numerical methods we employed. We argue that a core instability of 't Hooft Polyakov type monopoles is quite a generic feature of models with charged Higgs particles.Comment: Latex, 15 pages, 6 figures; published versio

On Sibling and Exceptional W Strings

We discuss the physical spectrum for $W$ strings based on the algebras $B_n$, $D_n$, $E_6$, $E_7$ and $E_8$. For a simply-laced $W$ string, we find a connection with the $(h,h+1)$ unitary Virasoro minimal model, where $h$ is the dual Coxeter number of the underlying Lie algebra. For the $W$ string based on $B_n$, we find a connection with the $(2h,2h+2)$ unitary $N=1$ super-Virasoro minimal model.Comment: 16 page

Bioinformatics

Motivation: Current methods that annotate conserved transcription factor binding sites in an alignment of two regulatory regions perform the alignment and annotation step separately and combine the results in the end. If the site descriptions are weak or the sequence similarity is low, the local gap structure of the alignment poses a problem in detecting the conserved sites. It is therefore desirable to have an approach that is able to simultaneously consider the alignment as well as possibly matching site locations. Results: With SimAnn we have developed a tool that serves exactly this purpose. By combining the annotation step and the alignment of the two sequences into one algorithm, it detects conserved sites more clearly. It has the additional advantage that all parameters are calculated based on statistical considerations. This allows for its successful application with any binding site model of interest. We present the algorithm and the approach for parameter selection and compare its performance with that of other, non-simultaneous methods on both simulated and real data. Availability: A command-line based C++ implementation of SimAnn is available from the authors upon request. In addition, we provide Perl scripts for calculating the input parameters based on statistical considerations

Null Fields Realizations of W3W_3 from W(sl(4),sl(3))W(sl(4),sl(3)) and W(sl(3∣1),sl(3))W(sl(3|1),sl(3)) Algebras

We consider the nonlinear algebras $W(sl(4),sl(3))$ and $W(sl(3|1),sl(3))$ and find their realizations in terms of currents spanning conformal linearizing algebras. The specific structure of these algebras, allows us to construct realizations modulo null fields of the $W_3$ algebra that lies in the cosets $W(sl(4),sl(3))/u(1)$ and $W(sl(3|1),sl(3))/u(1)$. Such realizations exist for the following values of the $W_3$ algebra central charge: $c_W=-30,-40/7,-98/5,-2$. The first two values are listed for the first time, whereas for the remaining values we get the new realizations in terms of an arbitrary stress tensor and $u(1)\times sl(2)$ affine currents.Comment: Submitted to Phys. Lett. B; PACS-no 11.30.L

COPING STRATEGIES OF THE FARM LABORERS TOWARD FARM MECHANIZATION IN CENTRAL, SAN JOSE, OCCIDENTAL MINDORO

This descriptive study was conducted to determine the coping strategies of farm laborers in San Jose, Occidental Mindoro towards farm mechanization. It was conducted at Barangay Central, San Jose, Occidental Mindoro, one of the top rice producing barangays in the province. The 123 of the 215 farm laborers listed in the different Kabesilya or farmers labor group were selected using simple random sampling. The farm laborers were engaged in planting and harvesting of rice for at least three years in Central, San Jose, Occidental Mindoro. The researcher used an interview schedule in gathering data. The study used descriptive statistics such as mean, frequency, and percentage. Pearson’s Product Moment Correlation was also used. Result shows that the farm laborers were in their middle aged, literate and with medium household size. The farm laborers generally “agree” that farm mechanization had affected their employment, food security level, education of children, monthly income, and agricultural production operations. The farm laborers “moderately practiced” the different coping strategies to meet the undesired effect of farm mechanization. Further, the “highly practiced” coping strategies were minimizing food expenses and seasonal migration of some household members to find odd jobs. Moreover, years spent in formal education and household size has a significant relationship on the extent of which farm laborers experience the effect of farm mechanization. Years spent in formal education have significant relationship on the coping strategies employed by farm laborers on advent of farm mechanization in the area

SU(3) monopoles and their fields

Some aspects of the fields of charge two SU(3) monopoles with minimal symmetry breaking are discussed. A certain class of solutions look like SU(2) monopoles embedded in SU(3) with a transition region or ``cloud'' surrounding the monopoles. For large cloud size the relative moduli space metric splits as a direct product AH\times R^4 where AH is the Atiyah-Hitchin metric for SU(2) monopoles and R^4 has the flat metric. Thus the cloud is parametrised by R^4 which corresponds to its radius and SO(3) orientation. We solve for the long-range fields in this region, and examine the energy density and rotational moments of inertia. The moduli space metric for these monopoles, given by Dancer, is also expressed in a more explicit form.Comment: 17 pages, 3 figures, latex, version appearing in Phys. Rev.