Minimal three-component SU(2) gadget for polarization optics

Two identities involving quarter-wave plates and half-wave plates are established. These are used to improve on an earlier gadget involving four wave plates leading to a new gadget involving just three plates, a half-wave plate and two quarter-wave plates, which can realize all SU(2) polarization transformations. This gadget is shown to involve the minimum number of quarter-wave and half-wave plates. The analysis leads to a decomposition theorem for SU (2) matrices in terms of factors which are symmetric fourth and eighth roots of the identity.

Coherence of the real symmetric Hardy algebra

Let D denote the open unit disk in C centered at 0. Let H-R(infinity) denote the set of all bounded and holomorphic functions defined in D that also satisfy f(z) = <(f <(z)over bar>)over bar> for all z is an element of D. It is shown that H-R(infinity) is a coherent ring.

Accelerating Numerical Linear Algebra Kernels on a Scalable Run Time Reconfigurable Platform

Numerical Linear Algebra (NLA) kernels are at the heart of all computational problems. These kernels require hardware acceleration for increased throughput. NLA Solvers for dense and sparse matrices differ in the way the matrices are stored and operated upon although they exhibit similar computational properties. While ASIC solutions for NLA Solvers can deliver high performance, they are not scalable, and hence are not commercially viable. In this paper, we show how NLA kernels can be accelerated on REDEFINE, a scalable runtime reconfigurable hardware platform. Compared to a software implementation, Direct Solver (Modified Faddeev's algorithm) on REDEFINE shows a 29X improvement on an average and Iterative Solver (Conjugate Gradient algorithm) shows a 15-20% improvement. We further show that solution on REDEFINE is scalable over larger problem sizes without any notable degradation in performance.

Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

Ampcalculator (AMPC) is a Mathematica (c) based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one loop (upto O(p(4))) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling G(27). Another illustrative set of amplitudes at tree level we provide is in the context of tau-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. The Kaon-Compton amplitude has been checked and a minor error in the published results has been pointed out. This exercise is a tutorial-based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics.

Structured Dispersion Matrices From Division Algebra Codes for Space-Time Shift Keying

We propose a novel method of constructing Dispersion Matrices (DM) for Coherent Space-Time Shift Keying (CSTSK) relying on arbitrary PSK signal sets by exploiting codes from division algebras. We show that classic codes from Cyclic Division Algebras (CDA) may be interpreted as DMs conceived for PSK signal sets. Hence various benefits of CDA codes such as their ability to achieve full diversity are inherited by CSTSK. We demonstrate that the proposed CDA based DMs are capable of achieving a lower symbol error ratio than the existing DMs generated using the capacity as their optimization objective function for both perfect and imperfect channel estimation.

Note on high aspect-ratio SU-8 micromechanical structures using mask-less direct laser writing

We report high aspect-ratio micromechanical structures made of SU-8 polymer, which is a negative photoresist. Mask-less direct writing with 405 nm laser is used to pattern spin-cast SU-8 films of thickness of more than 600 um. As compared with X-ray lithography, which helps pattern material to give aspect ratios of 1:50 or higher, laser writing is a less expensive and more accessible alternative. In this work, aspect ratios up to 1:30 were obtained on narrow pillars and cantilever structures. Deep vertical patterning was achieved in multiple exposures of the surface with varying dosages given at periodic intervals of sufficient duration. It was found that a time lag between successive exposures at the same location helps the material recover from the transient changes that occur during exposure to the laser. This gives vertical sidewalls to the resulting structures. The time-lags and dosages were determined by conducting several trials. The micromechanical structures obtained with laser writing are compared with those obtained with traditional UV lithography as well as e-beam lithography. Laser writing gives not only high aspect ratios but also narrow gaps whereas e-beam can only give narrow gaps over very small depths. Unlike traditional UV lithography, laser writing does not need a mask. Furthermore, there is no adjustment for varying the dosage in traditional UV lithography. A drawback of this method compared to UV lithography is that the writing time increases. Some test structures as well as a compliant microgripper are fabricated.

Quantum entropy for the fuzzy sphere and its monopoles

Using generalized bosons, we construct the fuzzy sphere S-F(2) and monopoles on S-F(2) in a reducible representation of SU(2). The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent nonabelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.

Baryon squishing in synthetic dimensions by effective SU(M) gauge fields

The ``synthetic dimension'' proposal A. Celi et al., Phys. Rev. Lett. 112, 043001 (2014)] uses atoms with M internal states (''flavors'') in a one-dimensional (1D) optical lattice, to realize a hopping Hamiltonian equivalent to the Hofstadter model (tight-binding model with a given magnetic flux per plaquette) on an M-sites-wide square lattice strip. We investigate the physics of SU(M) symmetric interactions in the synthetic dimension system. We show that this system is equivalent to particles with SU(M) symmetric interactions] experiencing an SU(M) Zeeman field at each lattice site and a non-Abelian SU(M) gauge potential that affects their hopping. This equivalence brings out the possibility of generating nonlocal interactions between particles at different sites of the optical lattice. In addition, the gauge field induces a flavor-orbital coupling, which mitigates the ``baryon breaking'' effect of the Zeeman field. For M particles, concomitantly, the SU(M) singlet baryon which is site localized in the usual 1D optical lattice, is deformed to a nonlocal object (''squished baryon''). We conclusively demonstrate this effect by analytical arguments and exact (numerical) diagonalization studies. Our study promises a rich many-body phase diagram for this system. It also uncovers the possibility of using the synthetic dimension system to laboratory realize condensed-matter models such as the SU(M) random flux model, inconceivable in conventional experimental systems.

MIXED NORM ESTIMATES FOR THE RIESZ TRANSFORMS ON SU (2)

In this paper we prove mixed norm estimates for Riesz transforms on the group SU(2). From these results vector valued inequalities for sequences of Riesz transforms associated to Jacobi differential operators of different types are deduced.

Evaluación temporal y espacial en el bosque de Pinus oocarpa Schiede y su impacto sobre la fijación de carbono en el municipio de Dipilto

El objetivo de este estudio fue a nalizar el cambio de uso de suelo durante un periodo de 18 años en las áreas de bosque de pino y su influencia en la fijación de bióxido de carbono en el Municipio de Dipilto, Nueva Segovia . Se seleccionaron 3 Fincas : San Martín, El Sarrete y Campofresco que presentaron estados de desarrollo: bosque maduro, bosque joven y bosque en regeneración. Se establecieron 9 parcelas temporales (con predominancia P. oocarpa ), utilizándose una parcela temporal para cada es tado d esarrollo. En cada estado de desarrollo se derribó un árbol tipo, se separó en tallo, ramas y follaje. La mayor par te de biomasa seca se encuentra en la finca San Martin con 99.12 Mg/ha estado en desarrollo maduro , estado en desarrollo joven con 77.70 Mg/ ha y estado en desarrollo regeneración 38.63 Mg/ha . El Factor de expansión de biomasa en San Martin 1.59 esta do en desarrollo regeneración, El Sarrete para el estado en desarrollo maduro 1 .40 y finca Campofresco 1.27 estado desarrollo joven . El total de ca rbono almacenado lo presentó San Martín para el estado en desarrollo maduro con 27.13 Mg/ha , joven 22.06 Mg/ha y estado en desarrollo regeneraci ón con 9.82 Mg/ha . El contenido de carbono en el suelo 826.89 Mg/ha regeneración, 503.96 Mg/ha Joven , 294.55 Mg/ ha maduro en San Martín de 0 a 20 cm de profundidad. En un 38.49 % de esa área se emitieron entre 0 - 15 Mg/ha . Emisiones de 26 - 30 Mg/ha se presentaron en un 17.8 1 % del área. Existe un 48.19 % del área total que fijo rangos de 26 - 30 Mg/ha y un 38. 49 % de las áreas fij aron entre 0 - 15 Mg /ha . Se encontró un balance neto positivo de 2925. 2 1 hectáreas, de las cuales 1981.25 hectáreas fijaron rangos de 26 - 30 Mg/ha, 606.06 hectáre as fijaron en un rango entre 0 - 15 Mg /ha y el rango 16 - 25 Mg/ha 337.89 hect áreas .