Zoology of Atlas-groups: dessins d'enfants, finite geometries and quantum commutation

Every finite simple group P can be generated by two of its elements. Pairs of generators for P are available in the Atlas of finite group representations as (not neccessarily minimal) permutation representations P. It is unusual but significant to recognize that a P is a Grothendieck's dessin d'enfant D and that most standard graphs and finite geometries G-such as near polygons and their generalizations-are stabilized by a D. In our paper, tripods P -- D -- G of rank larger than two, corresponding to simple groups, are organized into classes, e.g. symplectic, unitary, sporadic, etc (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurations defined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All the defined geometries G' s have a contextuality parameter close to its maximal value 1.Comment: 19 page

Poincar\'e polynomials for Abelian symplectic quotients of pure rr-qubits via wall-crossings

In this paper, we compute a recursive wall-crossing formula for the Poincar\'e polynomials and Euler characteristics of Abelian symplectic quotients of a complex projective manifold under a special effective action of a torus with non-trivial characters. An analogy can be made with the space of pure states of a composite quantum system containing $r$ quantum bits under action of the maximal torus of Local Unitary operations

Group-theoretic quantisation and central extensions

This work is concerned with the applications of Isham's group-theoretic quantisation programme to simple systems which involve central extensions of some symmetry group. Of particular interest are those systems with a 'Wess-Zumino'-like term in their actions where other nontrivial modifications are necessary. In Chapters 1 and 2, a review of the necessary tools used in this work as well as outlines of the group-theoretic quantisation programme are given to facilitate a smooth discussion in the latter chapters. The programme is first exemplified by the normal quantum mechanics on R". This example also involves central extensions but of a slightly different nature from those which arise from systems with a 'Wess-Zumino'-like term. Chapter 3 forms the core of the whole work. The discussions there provide the basis for further examples. It is concerned with the group-theoretic quantisation of the system of a particle moving on the two-torus in a constant magnetic field with quantised flux. The case without the magnetic field is also given for comparison. The canonical group for the case with the magnetic field is required to be the central extension of the universal cover of the canonical group for the case without the magnetic field. These results are then generalised to the corresponding systems on the n-torus. Chapter 4 is a digression from the main topic of quantisation and central extensions to the discussions of a-models with Wess-Zumino term. The main purpose of this chapter is to provide a parallel between these σ-models and the systems of a particle moving in a magnetic field (as in Chapter 3). The general construction of a Wess-Zumino term is given along with the discussion of an Abelian gauge symmetry that the term provides for the σ-models. The a-models can be interpreted as systems of a 'particle' moving on an infinite-dimensional configuration space in a background 'functional magnetic field'. This interpretation is further reinforced by the discussions of Noether's theorem and topological effects

Magnetized Bianchi type III massive string cosmological models in general relativity.

The present study deals with Bianchi type III string cosmological models with magnetic field. The magnetic field is assumed to be along z direction. Therefore F 12 is only the non-vanishing component of electromagnetic field tensor F ij . The expansion (θ) in the model is assumed to be proportional to the shear (σ). To get determinate solution in term of cosmic time, we have solved the fields equations in two cases (i) Reddy and (ii) Nambu string. The physical and geometrical behaviour of these models is discussed

Bianchi type-III string cosmological models for stiff and anti-stiff fluid in general relativity

Bianchi type-III string cosmological models in the presence of stiff and anti-stiff fluids are studied. The scalar expansion is assumed to be proportional to the shear. In the present study, we consider two cases (i)p+ρ= 0 and (ii) p−ρ= 0, where ρ and p are the rest energy density and the pressure of the fluid, respectively. The physical behavior of these models is also discussed

The application of data envelopment analysis and queuing models to large scale computer networks

This paper considers a technique for evaluating the operational efficiency of large-scale computer networks via data envelopment analysis and queuing models. The technique consists of two stages. In the second stage, a target DEA model is used which yield the advantages of the proposed technique over the previous one. Numerical illustration is provided to show the improvement of our aspect

An analysis of the Spekkens toy theory with connection to Wootters discrete phase space

The toy model of Spekkens is a formalism which can partially describe quantum mechanics. The theory deals with the (epistemic) states of a spin-1/2 particle, or qubits and it is closely related to the discrete phase space formalism of Wootters and collaborators. One can apply the stabilizer formalism for finding similarities of these two models. Noting that MUB basis vectors are obtained by eigenstates of generalized Pauli operators, the MUB basis vectors are thus the set of stabilizer states. Galvao has characterized the set of states with non-negative Wigner function class; they form the convex hull of the stabilizer states used as the MUB basis vectors. By combining both approaches, one can show epistemic states that are analogous to the convex hull of the stabilizer states (used as basis vectors in the MUB set) always make valid nonmaximal knowledge epistemic states

An Interacting Scenario for Dark Energy in Bianchi Type-I Universe

We study the interaction between dark energy (DE) and dark matter (DM) in the scope of anisotropic bianchi type I space-time. First we derive the general form of the dark energy equation of state parameter (EoS) in both non-interacting and interacting cases and then we examine it's future by applying a hyperbolic scale factor. It is shown that in non-interacting case, depending on the value of the anisotropy parameter $K$, the dark energy EoS parameter is varying from phantom to quintessence whereas in interacting case EoS parameter vary in quintessence region. However, in both cases the dark energy EoS parameter $\omega^{de}$, ultimately (i. e at $z=-1$) tends to the cosmological constant ($\omega^{de}=-1$). Moreover, we fixed the cosmological bound on the anisotropy parameter $K$ by using the recent observational data of Hubble parameter.Comment: 12 pages, 6 figures, Research in Astronomy and Astrophysics, 201

Two Dimensional Plane, Modified Symplectic Structure and Quantization

Noncommutative quantum mechanics on the plane has been widely studied in the literature. Here, we consider the problem using Isham's canonical group quantization scheme for which the primary object is the symmetry group that underlies the phase space. The noncommutativity of the configuration space coordinates requires us to introduce the noncommutative term in the symplectic structure of the system. This modified symplectic structure will modify the group acting on the configuration space from abelian $\mathbb{R}^2$ to a nonabelian one. As a result, the canonical group obtained is a deformed Heisenberg group and the canonical commutation relation (CCR) corresponds to what is usually found in noncommutative quantum mechanics.Comment: 5 pages. Submitted to Jurnal Fizik Malaysi