Unitarity Relations in c=1 Liouville Theory

We consider the S-matrix of c=1 Liouville theory with vanishing cosmological constant. We examine some of the constraints imposed by unitarity. These completely determine (N,2) amplitudes at tree level in terms of the (N,1) amplitudes when the plus tachyon momenta take generic values. A surprising feature of the matrix model results is the lack of particle creation branch cuts in the higher genus amplitudes. In fact, we show the naive field theory limit of Liouville theory would predict such branch cuts. However, unitarity in the full string theory ensures that such cuts do not appear in genus one (N,1) amplitudes. We conclude with some comments about the genus one (N,2) amplitudes.Comment: 14 pages, 3 figures (not included), phyzz

Proving causal relationships using observational data

We describe a means of rejecting a null hypothesis concerning observed, but not deliberately manipulated, variables of the form H0: A -/-> B in favor of an alternative hypothesis HA: A --> B, even given the possibility of causally related unobserved variables. Rejection of such an H0 relies on the availability of two observed and appropriately related instrumental variables. While the researcher will have limited control over the confidence level in this test, simulation results suggest that type I errors occur with a probability of less than 0.15 (often substantially less) across a wide range of circumstances. The power of the test is limited if there are but few observations available and the strength of correspondence among the variables is weak. We demonstrate the method by testing a hypothesis with critically important policy implications relating to a possible cause of childhood malnourishment.causality, Monte Carlo, observational data, hypothesis testing, Research Methods/ Statistical Methods,

Spin Readout Techniques of the Nitrogen-Vacancy Center in Diamond

The diamond nitrogen-vacancy (NV) center is a leading platform for quantum information science due to its optical addressability and room-temperature spin coherence. However, measurements of the NV center's spin state typically require averaging over many cycles to overcome noise. Here, we review several approaches to improve the readout performance and highlight future avenues of research that could enable single-shot electron-spin readout at room temperature.Comment: 21 pages, 7 figure

Cold-water coral reef frameworks, megafaunal communities and evidence for coral carbonate mounds on the Hatton Bank, north east Atlantic

Offshore banks and seamounts sustain diverse megafaunal communities, including framework reefs formed by cold-water corals. Few studies have quantified environmental effects on the alpha or beta diversity of these communities. We adopted an interdisciplinary approach that used historical geophysical data to identify topographic highs on Hatton Bank, which were surveyed visually. The resulting photographic data were used to examine relationships between megafaunal communities and macrohabitat, the latter defined into six categories (mud, sand, cobbles, coral rubble, coral framework, rock). The survey stations revealed considerable small-scale variability in macrohabitat from exposed Late Palaeocene lava flows to quiescent muddy habitats and coral-built carbonate mounds. The first reported evidence for coral carbonate mound development in UK waters is presented, which was most pronounced near present-day or former sites of topographic change, suggesting that local current acceleration favoured coral framework growth and mound initiation. Alpha diversity varied significantly across macrohabitats, but not between rock and coral rubble, or between smaller grain sized categories of cobbles, sand and mud. Community composition differed between most macrohabitats, and variation in beta diversity across Hatton Bank was largely explained by fine-scale substratum. Certain megafauna were clearly associated with particular macrohabitats, with stylasterid corals notably associated with cobble and rock habitats and coral habitats characterized by a diverse community of suspension-feeders. The visual surveys also produced novel images of deep-water megafauna including a new photographic record of the gorgonian coral Paragorgia arborea, a species not previously reported from Rockall Plateau. Further interdisciplinary studies are needed to interpret beta diversity across these and other environmental gradients on Hatton Bank. It is clear that efforts are also needed to improve our understanding of the genetic connectivity and biogeography of vulnerable deep-water ecosystems and to develop predictive models of their occurrence that can help inform future conservation measures

Conserved Quantities in Models of Classical Chaos

Quantum chaos is a major subject of interest in condensed matter theory, and has recently motivated new questions in the study of classical chaos. In particular, recent studies have uncovered interesting physics in the relationship between chaos and conserved quantities in models of quantum chaos. In this paper, we investigate this relationship in two simple models of classical chaos: the infinite-temperature Heisenberg spin chain, and the directed polymer in a random medium. We relate these models by drawing analogies between the energy landscape over which the directed polymer moves and the magnetization of the spin chain. We find that the coupling of the chaos to these conserved quantities results in, among other things, a marked transition from the rough perturbation profiles predicted by analogy to the KPZ equation to smooth, triangular profiles with reduced wandering exponents. These results suggest that diffusive conserved quantities can, in some cases, be the dominant forces shaping the development of chaos in classical systems.Comment: This was an undergraduate research paper by Henry Ando, which we are posting now because it is relevant to some continuing wor

Alignment-insensitive coupling for PLC-based surface mount photonics

A flip-chip waveguide coupler with an order of magnitude greater alignment tolerance than competing approaches is presented for the first time. Experimental data for an "optical jumper" agree with simple design considerations. Application to a planar lightwave circuit-based surface mount photonics platform is outlined