BRST invariance and de Rham-type cohomology of 't Hooft-Polyakov monopole

We exploit the 't Hooft-Polyakov monopole to define closed algebra of the quantum field operators and the BRST charge $Q_{BRST}$. In the first-class configuration of the Dirac quantization, by including the $Q_{BRST}$-exact gauge fixing term and the Faddeev-Popov ghost term, we find the BRST invariant Hamiltonian to investigate the de Rham-type cohomology group structure for the monopole system. The Bogomol'nyi bound is also discussed in terms of the first-class topological charge defined on the extended internal 2-sphere.Comment: 8 page

Provable Deterministic Leverage Score Sampling

We explain theoretically a curious empirical phenomenon: "Approximating a matrix by deterministically selecting a subset of its columns with the corresponding largest leverage scores results in a good low-rank matrix surrogate". To obtain provable guarantees, previous work requires randomized sampling of the columns with probabilities proportional to their leverage scores. In this work, we provide a novel theoretical analysis of deterministic leverage score sampling. We show that such deterministic sampling can be provably as accurate as its randomized counterparts, if the leverage scores follow a moderately steep power-law decay. We support this power-law assumption by providing empirical evidence that such decay laws are abundant in real-world data sets. We then demonstrate empirically the performance of deterministic leverage score sampling, which many times matches or outperforms the state-of-the-art techniques.Comment: 20th ACM SIGKDD Conference on Knowledge Discovery and Data Minin

Detailed Geant4 simulations of the ANITA and ANITA-CUP neutron facilities

Simulations of the ANITA spallation neutron source at The Svedberg Laboratory (TSL) are described. Neutron radiation calculations show close agreement with measurements at both standard and close user positions. Gamma radiation characteristics are also predicted

BRST extension of the Faddeev model

The Faddeev model is a second class constrained system. Here we construct its nilpotent BRST operator and derive the ensuing manifestly BRST invariant Lagrangian. Our construction employs the structure of Stuckelberg fields in a nontrivial fashion.Comment: 4 pages, new references adde

1.57 μm InGaAsP/InP surface emitting lasers by angled focus ion beam etching

The characteristics of 1.57 μm InGaAsP/InP surface emitting lasers based on an in-plan ridged structure and 45° beam deflectors defined by angled focused ion beam (FIB) etching are reported. With an externally integrated beam deflector, threshold currents and emission spectra identical to conventional edge emitting lasers are achieved. These results show that FIB etching is a very promising technique for the definition of high quality mirrors and beam deflectors on semiconductor heterostructures for a variety of integrated optoelectronic devices

The least common multiple of a sequence of products of linear polynomials

Let $f(x)$ be the product of several linear polynomials with integer coefficients. In this paper, we obtain the estimate: $\log {\rm lcm}(f(1), ..., f(n))\sim An$ as $n\rightarrow\infty$, where $A$ is a constant depending on $f$.Comment: To appear in Acta Mathematica Hungaric

Variational Approach to Hard Sphere Segregation Under Gravity

It is demonstrated that the minimization of the free energy functional for hard spheres and hard disks yields the result that excited granular materials under gravity segregate not only in the widely known "Brazil nut" fashion, i.e. with the larger particles rising to the top, but also in reverse "Brazil nut" fashion. Specifically, the local density approximation is used to investigate the crossover between the two types of segregation occurring in the liquid state, and the results are found to agree qualitatively with previously published results of simulation and of a simple model based on condensation.Comment: 10 pages, 3 figure

Finite-size scaling of synchronized oscillation on complex networks

The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and derive the corresponding scaling properties in the critical region. For scale-free networks with the degree distribution $P(k)\sim k^{-\gamma}$ at large $k$, we found that the finite size exponent $\bar{\nu}$ takes on the value 5/2 when $\gamma>5$, the same as in the globally coupled Kuramoto model. For highly heterogeneous networks ($3<\gamma <5$), $\bar{\nu}$ and the order parameter exponent $\beta$ depend on $\gamma$. The analytic expressions for these exponents obtained from the mean field theory are shown to be in excellent agreement with data from extensive numerical simulations.Comment: 7 page

Coupling of Josephson current qubits using a connecting loop

We propose a coupling scheme for the three-Josephson junction qubits which uses a connecting loop, but not mutual inductance. Present scheme offers the advantages of a large and tunable level splitting in implementing the controlled-NOT (CNOT) operation. We calculate the switching probabilities of the coupled qubits in the CNOT operations and demonstrate that present CNOT gate can meet the criteria for the fault-tolerant quantum computing. We obtain the coupling strength as a function of the coupling energy of the Josephson junction and the length of the connecting loop which varies with selecting two qubits from the scalable design.Comment: 5 pages with updates, version to appear in Phys. Rev.