Higgs transitions of spin ice

Frustrated magnets such as spin ice exhibit Coulomb phases, where correlations have power-law forms at long distances. Applied perturbations can cause ordering transitions which cannot be described by the usual Landau paradigm, and are instead naturally viewed as Higgs transitions of an emergent gauge theory. Starting from a classical statistical model of spin ice, it is shown that a variety of possible phases and transitions can be described by this approach. Certain cases are identified where continuous transitions are argued to be likely; the predicted critical behavior may be tested in experiments or numerical simulations.Comment: 23 pages, 10 figures; v2: published version with minor changes; ancillary file "Figures3D.nb" is a Mathematica (v7) notebook containing figures as rotatable 3D graphics (see http://www.wolfram.com/cdf-player/ for a free viewer

Mechanical properties of brittle materials

Brittle materials are difficult to tensile test because of gripping problems. They either crack in conventional grips or they are crushed. Furthermore, they may be difficult to make into tensile specimens having, for example, threated ends or donut shapes. To overcome the problem, simple rectangular shapes can be used in bending (i.e., a simple beam) in order to obtain the modulus of rupture and the elastic modulus. The equipment necessary consists of a fixture for supporting the specimens horizontally at two points, these points contact points being rollers which are free to rotate. The force necessary to bend the specimen is produced by a tup attached to the crosshead of an Instron machine. Here, the experimental procedure is explained

Microarcsecond Radio Imaging using Earth Orbit Synthesis

The observed interstellar scintillation pattern of an intra-day variable radio source is influenced by its source structure. If the velocity of the interstellar medium responsible for the scattering is comparable to the earth's, the vector sum of these allows an observer to probe the scintillation pattern of a source in two dimensions and, in turn, to probe two-dimensional source structure on scales comparable to the angular scale of the scintillation pattern, typically $\sim 10 \mu$as for weak scattering. We review the theory on the extraction of an ``image'' from the scintillation properties of a source, and show how earth's orbital motion changes a source's observed scintillation properties during the course of a year. The imaging process, which we call Earth Orbit Synthesis, requires measurements of the statistical properties of the scintillations at epochs spread throughout the course of a year.Comment: ApJ in press. 25 pages, 7 fig

Obstructions to Lagrangian concordance

We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in R3. In particular, we give obstructions to a concordance from an arbitrary knot to the standard Legendrian unknot, in terms of normal rulings. We also place strong restrictions on knots that have concordances both to and from the unknot and construct an infinite family of knots with nonreversible concordances from the unknot. Finally, we use our obstructions to present a complete list of knots with up to 14 crossings that have Legendrian representatives that are Lagrangian slice

Leaf Traits Within Communities: Context May Affect the Mapping of Traits to Function

The leaf economics spectrum (LES) has revolutionized the way many ecologists think about quantifying plant ecological trade-offs. In particular, the LES has connected a clear functional trade-off (long-lived leaves with slow carbon capture vs. short-lived leaves with fast carbon capture) to a handful of easily measured leaf traits. Building on this work, community ecologists are now able to quickly assess species carbon-capture strategies, which may have implications for community-level patterns such as competition or succession. However, there are a number of steps in this logic that require careful examination, and a potential danger arises when interpreting leaf-trait variation among species within communities where trait relationships are weak. Using data from 22 diverse communities, we show that relationships among three common functional traits (photosynthetic rate, leaf nitrogen concentration per mass, leaf mass per area) are weak in communities with low variation in leaf life span (LLS), especially communities dominated by herbaceous or deciduous woody species. However, globally there are few LLS data sets for communities dominated by herbaceous or deciduous species, and more data are needed to confirm this pattern. The context-dependent nature of trait relationships at the community level suggests that leaf-trait variation within communities, especially those dominated by herbaceous and deciduous woody species, should be interpreted with caution

Parameter Estimation with Mixed-State Quantum Computation

We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H= \theta H_0$, we estimate $\theta$ by zooming in on previous estimations and by implementing an adaptive Bayesian procedure. The final result of the algorithm is an updated estimation of $\theta$ whose variance has been decreased in proportion to the time of evolution under H. For the problem of estimating several parameters, we implement dynamical-decoupling techniques and use the results of single parameter estimation. The cases of discrete-time evolution and reference-frame alignment are also discussed within the adaptive approach.Comment: 12 pages. Improved introduction and technical details moved to Appendi

Ionospheric Power-Spectrum Tomography in Radio Interferometry

A tomographic method is described to quantify the three-dimensional power-spectrum of the ionospheric electron-density fluctuations based on radio-interferometric observations by a two-dimensional planar array. The method is valid to first-order Born approximation and might be applicable to correct observed visibilities for phase variations due to the imprint of the full three-dimensional ionosphere. It is shown that not the ionospheric electron density distribution is the primary structure to model in interferometry, but its autocorrelation function or equivalent its power-spectrum. An exact mathematical expression is derived that provides the three dimensional power-spectrum of the ionospheric electron-density fluctuations directly from a rescaled scattered intensity field and an incident intensity field convolved with a complex unit phasor that depends on the w-term and is defined on the full sky pupil plane. In the limit of a small field of view, the method reduces to the single phase screen approximation. Tomographic self-calibration can become important in high-dynamic range observations at low radio frequencies with wide-field antenna interferometers, because a three-dimensional ionosphere causes a spatially varying convolution of the sky, whereas a single phase screen results in a spatially invariant convolution. A thick ionosphere can therefore not be approximated by a single phase screen without introducing errors in the calibration process. By applying a Radon projection and the Fourier projection-slice theorem, it is shown that the phase-screen approach in three dimensions is identical to the tomographic method. Finally we suggest that residual speckle can cause a diffuse intensity halo around sources, due to uncorrectable ionospheric phase fluctuations in the short integrations, which could pose a fundamental limit on the dynamic range in long-integration images.Comment: 8 pages; Accepted for publication in Ap

Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians

We introduce several exact models for SU(3) spin chains: (1) a translationally invariant parent Hamiltonian involving four-site interactions for the trimer chain, with a three-fold degenerate ground state. We provide numerical evidence that the elementary excitations of this model transform under representation 3bar of SU(3) if the original spins of the model transform under rep. 3. (2) a family of parent Hamiltonians for valence bond solids of SU(3) chains with spin reps. 6, 10, and 8 on each lattice site. We argue that of these three models, only the latter two exhibit spinon confinement and a Haldane gap in the excitation spectrum

Efficient solvability of Hamiltonians and limits on the power of some quantum computational models

We consider quantum computational models defined via a Lie-algebraic theory. In these models, specified initial states are acted on by Lie-algebraic quantum gates and the expectation values of Lie algebra elements are measured at the end. We show that these models can be efficiently simulated on a classical computer in time polynomial in the dimension of the algebra, regardless of the dimension of the Hilbert space where the algebra acts. Similar results hold for the computation of the expectation value of operators implemented by a gate-sequence. We introduce a Lie-algebraic notion of generalized mean-field Hamiltonians and show that they are efficiently ("exactly") solvable by means of a Jacobi-like diagonalization method. Our results generalize earlier ones on fermionic linear optics computation and provide insight into the source of the power of the conventional model of quantum computation.Comment: 6 pages; no figure