Modelling gravity on a hyper-cubic lattice

We present an elegant and simple dynamical model of symmetric, non-degenerate (n x n) matrices of fixed signature defined on a n-dimensional hyper-cubic lattice with nearest-neighbor interactions. We show how this model is related to General Relativity, and discuss multiple ways in which it can be useful for studying gravity, both classical and quantum. In particular, we show that the dynamics of the model when all matrices are close to the identity corresponds exactly to a finite-difference discretization of weak-field gravity in harmonic gauge. We also show that the action which defines the full dynamics of the model corresponds to the Einstein-Hilbert action to leading order in the lattice spacing, and use this observation to define a lattice analogue of the Ricci scalar and Einstein tensor. Finally, we perform a mean-field analysis of the statistical mechanics of this model.Comment: 5 page

Composite fermion wave functions as conformal field theory correlators

It is known that a subset of fractional quantum Hall wave functions has been expressed as conformal field theory (CFT) correlators, notably the Laughlin wave function at filling factor $\nu=1/m$ ($m$ odd) and its quasiholes, and the Pfaffian wave function at $\nu=1/2$ and its quasiholes. We develop a general scheme for constructing composite-fermion (CF) wave functions from conformal field theory. Quasiparticles at $\nu=1/m$ are created by inserting anyonic vertex operators, $P_{\frac{1}{m}}(z)$, that replace a subset of the electron operators in the correlator. The one-quasiparticle wave function is identical to the corresponding CF wave function, and the two-quasiparticle wave function has correct fractional charge and statistics and is numerically almost identical to the corresponding CF wave function. We further show how to exactly represent the CF wavefunctions in the Jain series $\nu = s/(2sp+1)$ as the CFT correlators of a new type of fermionic vertex operators, $V_{p,n}(z)$, constructed from $n$ free compactified bosons; these operators provide the CFT representation of composite fermions carrying $2p$ flux quanta in the $n^{\rm th}$ CF Landau level. We also construct the corresponding quasiparticle- and quasihole operators and argue that they have the expected fractional charge and statistics. For filling fractions 2/5 and 3/7 we show that the chiral CFTs that describe the bulk wave functions are identical to those given by Wen's general classification of quantum Hall states in terms of $K$-matrices and $l$- and $t$-vectors, and we propose that to be generally true. Our results suggest a general procedure for constructing quasiparticle wave functions for other fractional Hall states, as well as for constructing ground states at filling fractions not contained in the principal Jain series.Comment: 26 pages, 3 figure

Differential plant invasiveness is not always driven by host promiscuity with bacterial symbionts

Identification of mechanisms that allow some species to outcompete others is a fundamental goal in ecology and invasive species management. One useful approach is to examine congeners varying in invasiveness in a comparative framework across native and invaded ranges. Acacia species have been widely introduced outside their native range of Australia, and a subset of these species have become invasive in multiple parts of the world. Within specific regions, the invasive status of these species varies. Our study examined whether a key mechanism in the life history of Acacia species, the legume-rhizobia symbiosis, influences acacia invasiveness on a regional scale. To assess the extent to which species varying in invasiveness correspondingly differ with regard to the diversity of rhizobia they associate with, we grew seven Acacia species ranging in invasiveness in California in multiple soils from both their native (Australia) and introduced (California) ranges. In particular, the aim was to determine whether more invasive species formed symbioses with a wider diversity of rhizobial strains (i.e. are more promiscuous hosts). We measured and compared plant performance, including aboveground biomass, survival, and nodulation response, as well as rhizobial community composition and richness. Host promiscuity did not differ among invasiveness categories. Acacia species that varied in invasiveness differed in aboveground biomass for only one soil and did not differ in survival or nodulation within individual soils. In addition, acacias did not differ in rhizobial richness among invasiveness categories. However, nodulation differed between regions and was generally higher in the native than introduced range. Our results suggest that all Acacia species introduced to California are promiscuous hosts and that host promiscuity per se does not explain the observed differences in invasiveness within this region. Our study also highlights the utility of assessing potential mechanisms of invasion in species’ native and introduced ranges

Host promiscuity in symbiont associations can influence exotic legume establishment and colonization of novel ranges

Aim Invasive Acacia species have negatively impacted natural areas in multiple regions around the globe. Almost 400 Acacia species have been introduced outside their native ranges in Australia; approximately 6% have become invasive, 12% are naturalized, and 82% have no record of naturalization or invasion. This variation in invasiveness provides a comparative framework in which to examine mechanisms that either promote or constrain establishment and colonization of species in novel regions. Here, we experimentally examine the role that the legume–rhizobia symbiosis plays in the differential invasiveness of acacias introduced outside their native Australian ranges. Location Canberra, Australia. Methods We paired 12 Acacia species ranging in invasiveness globally with 12 rhizobial strains ranging in average symbiotic effectiveness. We measured plant growth and nodulation success and abundance to assess whether invasive acacias were more promiscuous hosts, that is had positive growth and nodulation responses to a broader range of rhizobial strains than naturalized and non-invasive species. Results Invasive acacias had a higher growth response across more rhizobial strains (six of 12 strains) than naturalized and non-invasive species, but invasiveness categories differed only moderately with regard to the percentage of plants with nodules and nodulation abundance. Main conclusion With respect to plant growth, invasive acacias appear to be more promiscuous hosts than naturalized and non-invasive Australian Acacia species. Plant growth response to nodulation, however, is likely more important than nodulation alone in the successful invasion of species in novel ranges. Results from this study help elucidate an important mechanism in the invasive capacity of legumes

Random Matrix Theory Analysis of Cross Correlations in Financial Markets

We confirm universal behaviors such as eigenvalue distribution and spacings predicted by Random Matrix Theory (RMT) for the cross correlation matrix of the daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been reported for New York Stock Exchange in previous studies. It is shown that the random part of the eigenvalue distribution of the cross correlation matrix is stable even when deterministic correlations are present. Some deviations in the small eigenvalue statistics outside the bounds of the universality class of RMT are not completely explained with the deterministic correlations as proposed in previous studies. We study the effect of randomness on deterministic correlations and find that randomness causes a repulsion between deterministic eigenvalues and the random eigenvalues. This is interpreted as a reminiscent of ``level repulsion'' in RMT and explains some deviations from the previous studies observed in the market data. We also study correlated groups of issues in these markets and propose a refined method to identify correlated groups based on RMT. Some characteristic differences between properties of Tokyo Stock Exchange and New York Stock Exchange are found.Comment: RevTex, 17 pages, 8 figure

Magneto-polarisability of mesoscopic rings

We calculate the average polarisability of two dimensional mesoscopic rings in the presence of an Aharonov-Bohm flux. The screening is taken into account self-consistently within a mean-field approximation. We investigate the effects of statistical ensemble, finite frequency and disorder. We emphasize geometrical effects which make the observation of field dependent polarisability much more favourable on rings than on disks or spheres of comparable radius. The ratio of the flux dependent to the flux independent part is estimated for typical GaAs rings.Comment: pages, Revtex, 1 eps figur

Availability of soil mutualists may not limit non‐native Acacia invasion but could increase their impact on native soil communities

The availability of compatible mutualistic soil microbes could influence the invasion success of non-native plant species. Specifically, there may be spatial variation in the distribution of compatible microbes, and species-specific variation in plant host ability to associate with available microbes. Although either or both factors could promote or limit invasion, the scale over which most studies are conducted makes it difficult to examine these two possibilities simultaneously. However, this is critical to identifying a role of soil microbes in invasion. A series of recent research projects focused on interactions between Australian Acacia and nitrogen-fixing bacteria (rhizobia) at multiple spatial scales, from the local to the inter-continental, has allowed us to evaluate this question. Collectively, this research reveals that nodulation, performance and rhizobial community composition are all broadly similar across spatial scales and differentially invasive species. Synthesis and applications. We argue that current research provides convincing evidence that interactions with rhizobia do not determine invasion success in Acacia, but instead highlights key knowledge gaps that remain unfilled. Importantly, the ease with which non-native Acacia species form mutualistic associations with rhizobia, regardless of invasive status, highlights the critical need to understand the impacts of all non-native Acacia on native soil communities

Solitons and Quasielectrons in the Quantum Hall Matrix Model

We show how to incorporate fractionally charged quasielectrons in the finite quantum Hall matrix model.The quasielectrons emerge as combinations of BPS solitons and quasiholes in a finite matrix version of the noncommutative $\phi^4$ theory coupled to a noncommutative Chern-Simons gauge field. We also discuss how to properly define the charge density in the classical matrix model, and calculate density profiles for droplets, quasiholes and quasielectrons.Comment: 15 pages, 9 figure

Factors influencing the catalytic oxidation of benzyl alcohol using supported phosphine-capped gold nanoparticles

Open Access Article. This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.Two phosphine-stabilised gold clusters, Au101(PPh3)21Cl5 and Au9(PPh3)8(NO3)3, were deposited and activated on anatase TiO2 and fumed SiO2. These catalysts showed an almost complete oxidation of benzyl alcohol (>90%) within 3 hours at 80 °C and 3 bar O2 in methanol with a high substrate-to-metal molar ratio of 5800 and turn-over frequency of 0.65 s−1. Factors influencing catalytic activity were investigated, including metal–support interaction, effects of heat treatments, chemical composition of gold clusters, the size of gold nanoparticles and catalytic conditions. It was found that the anions present in gold clusters play a role in determining the catalytic activity in this reaction, with NO3− diminishing the catalytic activity. High catalytic activity was attributed to the formation of large gold nanoparticles (>2 nm) that coincides with partial removal of ligands which occurs during heat treatment and catalysis. Selectivity towards the formation of methyl benzoate can be tuned by selection of the reaction temperature. The catalysts were characterised using transmission electron microscopy, UV-vis diffuse reflectance spectroscopy and X-ray photoelectron spectroscopy

Statistical Properties of Cross-Correlation in the Korean Stock Market

We investigate the statistical properties of the correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The $\beta_{473}$ coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function $E(\sigma)$ with the portfolio risk $\sigma$ for the original and filtered correlation matrices are consistent with a power-law function, $E(\sigma) \sim \sigma^{-\gamma}$, with the exponent $\gamma \sim 2.92$ and those for Asian currency crisis decreases significantly