Isomonodromic deformatiion with an irregular singularity and hyperelliptic curve

In this paper, we extend the result of Kitaev and Korotkin to the case where a monodromy-preserving deformation has an irregular singularity. For the monodromy-preserving deformation, we obtain the $\tau$-function whose deformation parameters are the positions of regular singularities and the parameter $t$ of an irregular singularity. Furthermore, the $\tau$-function is expressed by the hyperelliptic $\Theta$ function moving the argument \z and the period \B, where $t$ and the positions of regular singularities move $z$ and \B, respectively.Comment: 23 pages, 2 figure

Semiclassical Strings in AdS_5 x S^5 and Automorphic Functions

Using AdS/CFT we derive from the folded spinning string ordinary differential equations for the anomalous dimension of the dual N=4 SYM twist-two operators at strong coupling. We show that for large spin the asymptotic solutions have the Gribov-Lipatov recirocity property. To obtain this result we use a hidden modular invariance of the energy-spin relation of the folded spinning string. Further we identify the Moch-Vermaseren-Vogt (MVV) relations, which were first recognized in plain QCD calculations, as the recurrence relations of the asymptotic series ansatz.Comment: 4 page

Low Rank Vector Bundles on the Grassmannian G(1,4)

Here we define the concept of $L$-regularity for coherent sheaves on the Grassmannian G(1,4) as a generalization of Castelnuovo-Mumford regularity on ${\bf{P}^n}$. In this setting we prove analogs of some classical properties. We use our notion of $L$-regularity in order to prove a splitting criterion for rank 2 vector bundles with only a finite number of vanishing conditions. In the second part we give the classification of rank 2 and rank 3 vector bundles without "inner" cohomology (i.e. H^i_*(E)=H^i(E\otimes\Q)=0 for any $i=2,3,4$) on G(1,4) by studying the associated monads.Comment: 11 pages, no figure

Topological quantum gate entangler for a multi-qubit state

We establish a relation between topological and quantum entanglement for a multi-qubit state by considering the unitary representations of the Artin braid group. We construct topological operators that can entangle multi-qubit state. In particular we construct operators that create quantum entanglement for multi-qubit states based on the Segre ideal of complex multi-projective space. We also in detail discuss and construct these operators for two-qubit and three-qubit states.Comment: 6 page

Impurity in a Bose-Einstein condensate in a double well

We compare and contrast the mean-field and many-body properties of a Bose-Einstein condensate trapped in a double well potential with a single impurity atom. The mean-field solutions display a rich structure of bifurcations as parameters such as the boson-impurity interaction strength and the tilt between the two wells are varied. In particular, we study a pitchfork bifurcation in the lowest mean-field stationary solution which occurs when the boson-impurity interaction exceeds a critical magnitude. This bifurcation, which is present for both repulsive and attractive boson-impurity interactions, corresponds to the spontaneous formation of an imbalance in the number of particles between the two wells. If the boson-impurity interaction is large, the bifurcation is associated with the onset of a Schroedinger cat state in the many-body ground state. We calculate the coherence and number fluctuations between the two wells, and also the entanglement entropy between the bosons and the impurity. We find that the coherence can be greatly enhanced at the bifurcation.Comment: 19 pages, 17 figures. The second version contains minor corrections and some better figures (thicker lines

Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata

Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is the union of a finite set of strata, which are semialgebraic manifolds formed by the $G$-orbits with the same orbit-type. In this paper we provide a simple recipe to obtain rational parametrizations of the strata. Our results can be easily exploited, in many physical contexts where the study of equivariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry breaking, in the analysis of phase spaces and structural phase transitions (Landau theory), in equivariant bifurcation theory, in crystal field theory and in most areas where use is made of symmetry adapted functions. A physically significant example of utilization of the recipe is given, related to spontaneous polarization in chiral biaxial liquid crystals, where the advantages with respect to previous heuristic approaches are shown.Comment: Figures generated through texdraw package; revised version appearing in J. Phys. A: Math. Ge

Collective leadership behaviors : evaluating the leader, team network, and problem situation characteristics that influence their use

The focus on non-hierarchical, collectivistic, leadership has been steadily increasing with several different theories emerging (Yammarino, Salas, Serban, Shirreffs, & Shuffler, 2012). While most take the view that collectivistic approaches to leadership (e.g., shared and distributed leadership) are emergent properties of the team, a recent, integrative framework by Friedrich, Vessey, Schuelke, Ruark and Mumford (2009) proposed that collective leadership, defined as the selective utilization of expertise within the network, does not eliminate the role of the focal leader. In the present study, three dimensions of collective leadership behaviors from the Friedrich et al. (2009) framework — Communication, Network Development, and Leader–Team Exchange were tested with regard to how individual differences of leaders (intelligence, experience, and personality), the team's network (size, interconnectedness, and embeddedness), the given problem domain (strategic change or innovation), and problem focus (task or relationship focused) influenced the use of each collective leadership dimension

Development of probabilistic models for quantitative pathway analysis of plant pest introduction for the EU territory

This report demonstrates a probabilistic quantitative pathway analysis model that can be used in risk assessment for plant pest introduction into EU territory on a range of edible commodities (apples, oranges, stone fruits and wheat). Two types of model were developed: a general commodity model that simulates distribution of an imported infested/infected commodity to and within the EU from source countries by month; and a consignment model that simulates the movement and distribution of individual consignments from source countries to destinations in the EU. The general pathway model has two modules. Module 1 is a trade pathway model, with a Eurostat database of five years of monthly trade volumes for each specific commodity into the EU28 from all source countries and territories. Infestation levels based on interception records, commercial quality standards or other information determine volume of infested commodity entering and transhipped within the EU. Module 2 allocates commodity volumes to processing, retail use and waste streams and overlays the distribution onto EU NUTS2 regions based on population densities and processing unit locations. Transfer potential to domestic host crops is a function of distribution of imported infested product and area of domestic production in NUTS2 regions, pest dispersal potential, and phenology of susceptibility in domestic crops. The consignment model covers the several routes on supply chains for processing and retail use. The output of the general pathway model is a distribution of estimated volumes of infested produce by NUTS2 region across the EU28, by month or annually; this is then related to the accessible susceptible domestic crop. Risk is expressed as a potential volume of infested fruit in potential contact with an area of susceptible domestic host crop. The output of the consignment model is a volume of infested produce retained at each stage along the specific consignment trade chain

Moduli of mathematical instanton vector bundles with odd c_2 on projective space

The problem of irreducibility of the moduli space I_n of rank-2 mathematical instanton vector bundles with arbitrary positive second Chern class n on the projective 3-space is considered. The irreducibility of I_n was known for small values of n: Barth 1977 (n=1), Hartshorne 1978 (n=2), Ellingsrud and Stromme 1981 (n=3), Barth 1981 (n=4), Coanda, Tikhomirov and Trautmann 2003 (n=5). In this paper we prove the irreducibility of I_n for an arbitrary odd n.Comment: 62 page

Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids

Many trial wavefunctions for fractional quantum Hall states in a single Landau level are given by functions called conformal blocks, taken from some conformal field theory. Also, wavefunctions for certain paired states of fermions in two dimensions, such as p_x+ip_y states, reduce to such a form at long distances. Here we investigate the adiabatic transport of such many-particle trial wavefunctions using methods from two-dimensional field theory. One context for this is to calculate the statistics of widely-separated quasiholes, which has been predicted to be non-Abelian in a variety of cases. The Berry phase or matrix (holonomy) resulting from adiabatic transport around a closed loop in parameter space is the same as the effect of analytic continuation around the same loop with the particle coordinates held fixed (monodromy), provided the trial functions are orthonormal and holomorphic in the parameters so that the Berry vector potential (or connection) vanishes. We show that this is the case (up to a simple area term) for paired states (including the Moore-Read quantum Hall state), and present general conditions for it to hold for other trial states (such as the Read-Rezayi series). We argue that trial states based on a non-unitary conformal field theory do not describe a gapped topological phase, at least in many cases. By considering adiabatic variation of the aspect ratio of the torus, we calculate the Hall viscosity, a non-dissipative viscosity coefficient analogous to Hall conductivity, for paired states, Laughlin states, and more general quantum Hall states. Hall viscosity is an invariant within a topological phase, and is generally proportional to the "conformal spin density" in the ground state.Comment: 44 pages, RevTeX; v2 minor changes; v3 typos corrected, three small addition