On the Solutions of Generalized Bogomolny Equations

Generalized Bogomolny equations are encountered in the localization of the topological N=4 SYM theory. The boundary conditions for 't Hooft and surface operators are formulated by giving a model solution with some special singularity. In this note we consider the generalized Bogomolny equations on a half space and construct model solutions for the boundary 't Hooft and surface operators. It is shown that for the 't Hooft operator the equations reduce to the open Toda chain for arbitrary simple gauge group. For the surface operators the solutions of interest are rational solutions of a periodic non-abelian Toda system.Comment: 16 pages, no figure

Anomaly-Free Supersymmetric SO(2N+2)/U(N+1) sigma-Model Based on the SO(2N+1) Lie Algebra of the Fermion Operators

The extended supersymmetric (SUSY) sigma-model has been proposed on the bases of SO(2N+1) Lie algebra spanned by fermion annihilation-creation operators and pair operators. The canonical transformation, extension of an SO(2N) Bogoliubov transformation to an SO(2N+1) group, is introduced. Embedding the SO(2N+1) group into an SO(2N+2) group and using SO(2N+2)/U(N+1) coset variables, we have investigated the SUSY sigma-model on the Kaehler manifold, the coset space SO(2N+2)/U(N+1). We have constructed the Killing potential, extension of the potential in the SO(2N)/U(N) coset space to that in the SO(2N+2)/U(N+1) coset space. It is equivalent to the generalized density matrix whose diagonal-block part is related to a reduced scalar potential with a Fayet-Ilipoulos term. The f-deformed reduced scalar potential is optimized with respect to vacuum expectation value of the sigma-model fields and a solution for one of the SO(2N+1) group parameters has been obtained. The solution, however, is only a small part of all solutions obtained from anomaly-free SUSY coset models. To construct the coset models consistently, we must embed a coset coordinate in an anomaly-free spinor representation (rep) of SO(2N+2) group and give corresponding Kaehler and Killing potentials for an anomaly-free SO(2N+2)/U(N+1) model based on each positive chiral spinor rep. Using such mathematical manipulation we construct successfully the anomaly-free SO(2N+2)/U(N+1) SUSY sigma-model and investigate new aspects which have never been seen in the SUSY sigma-model on the Kaehler coset space SO(2N)/U(N). We reach a f-deformed reduced scalar potential. It is minimized with respect to the vacuum expectation value of anomaly-free SUSY sigma-model fields. Thus we find an interesting f-deformed solution very different from the previous solution for an anomaly-free SO(2.5+2)/(SU(5+1)*U(1)) SUSY sigma-model.Comment: 24 pages, no fiure

On Hilbert-Schmidt operator formulation of noncommutative quantum mechanics

This work gives value to the importance of Hilbert-Schmidt operators in the formulation of a noncommutative quantum theory. A system of charged particle in a constant magnetic field is investigated in this framework

Shape invariant potential formalism for photon-added coherent state construction

An algebro-operator approach, called shape invariant potential method, of constructing generalized coherent states for photon-added particle system is presented. Illustration is given on Poschl-Teller potential

Classical and Quantum Solitons in the Symmetric Space Sine-Gordon Theories

We construct the soliton solutions in the symmetric space sine-Gordon theories. The latter are a series of integrable field theories in 1+1-dimensions which are associated to a symmetric space F/G, and are related via the Pohlmeyer reduction to theories of strings moving on symmetric spaces. We show that the solitons are kinks that carry an internal moduli space that can be identified with a particular co-adjoint orbit of the unbroken subgroup H of G. Classically the solitons come in a continuous spectrum which encompasses the perturbative fluctuations of the theory as the kink charge becomes small. We show that the solitons can be quantized by allowing the collective coordinates to be time-dependent to yield a form of quantum mechanics on the co-adjoint orbit. The quantum states correspond to symmetric tensor representations of the symmetry group H and have the interpretation of a fuzzy geometric version of the co-adjoint orbit. The quantized finite tower of soliton states includes the perturbative modes at the base.Comment: 53 pages, additional comments and small errors corrected, final journal versio

Quantum Computation with Coherent Spin States and the Close Hadamard Problem

We study a model of quantum computation based on the continuously-parameterized yet finite-dimensional Hilbert space of a spin system. We explore the computational powers of this model by analyzing a pilot problem we refer to as the close Hadamard problem. We prove that the close Hadamard problem can be solved in the spin system model with arbitrarily small error probability in a constant number of oracle queries. We conclude that this model of quantum computation is suitable for solving certain types of problems. The model is effective for problems where symmetries between the structure of the information associated with the problem and the structure of the unitary operators employed in the quantum algorithm can be exploited.Comment: RevTeX4, 13 pages with 8 figures. Accepted for publication in Quantum Information Processing. Article number: s11128-015-1229-

Highly symmetric POVMs and their informational power

We discuss the dependence of the Shannon entropy of normalized finite rank-1 POVMs on the choice of the input state, looking for the states that minimize this quantity. To distinguish the class of measurements where the problem can be solved analytically, we introduce the notion of highly symmetric POVMs and classify them in dimension two (for qubits). In this case we prove that the entropy is minimal, and hence the relative entropy (informational power) is maximal, if and only if the input state is orthogonal to one of the states constituting a POVM. The method used in the proof, employing the Michel theory of critical points for group action, the Hermite interpolation and the structure of invariant polynomials for unitary-antiunitary groups, can also be applied in higher dimensions and for other entropy-like functions. The links between entropy minimization and entropic uncertainty relations, the Wehrl entropy and the quantum dynamical entropy are described.Comment: 40 pages, 3 figure

Removal of organic matter from reservoir water: mechanisms underpinning surface chemistry of natural adsorbents

One of the key challenges in water treatment industry is the removal of organic compounds by cost-effective methods. This study evaluated the adsorptive removal of dissolved organic carbon (DOC) from reservoir water using fuller’s earth (FE) in comparison with natural (SQ) and modified quartz (MSQ) sands. The removal capacities of FE at different contact times, pH levels, adsorbent dosages and initial DOC concentrations were compared with both the quartz sands. The optimum DOC removals by FE and SQs were achieved at contact time of 60 and 30 min, pH level of 6 and 4, and at adsorbent dose of 1.5 g/150 mL and 10 g/100 mL, respectively. The adsorption capacity of FE (1.05 mg/g) was much higher compared to the MSQ (0.04 mg/g) and SQ (0.01 mg/g). Adsorption equilibrium data better fitted to the Freundlich model than to the Langmuir model, suggesting that adsorption occurred primarily through multilayer formation onto the surfaces of FE and SQ. The pseudo-second-order model described the uptake kinetics more effectively than the pseudo-first-order and intra-particle diffusion models, indicating that the mechanism was primarily governed by chemisorption. These observations were well supported by the physiochemical characteristics and charge behaviour of the adsorbents. In mass-transfer study, the results of liquid film diffusion model showed that the adsorption of DOC on FE was not controlled by film diffusion, but other mechanisms also played an essential role. This study demonstrates that FE is an effective adsorbent for the removal of DOC in surface water treatment