Winding clusters in percolation on the Torus and the Moebius strip

Using a simulation technique introduced recently, we study winding clusters in percolation on the torus and the Moebius strip for different aspect ratios. The asynchronous parallelization of the simulation makes very large system and sample sizes possible. Our high accuracy results are fully consistent with predictions from conformal field theory. The numerical results for the Moebius strip and the number distribution of winding clusters on the torus await theoretical explanation. To our knowledge, this study is the first of its kind.Comment: 20 pages, 9 figures, submitted to J. Stat. Phy

Comment on: "Superscaling of Percolation on Rectangular Domains"

In [Watanabe et al., Phys. Rev. Lett. 93 190601 (2004)], the authors show numerically that spanning and percolation probabilities in two-dimensional systems with different aspect ratios obey a form of "superscaling". In this comment, we would like to point out some difficulties with their proposed scaling ansatz and suggest why this remained undetected in their numerical analysis.Comment: 1 page + references, 1 figur

Composite fermion dynamics in half-filled Landau levels of graphene

We report on exact-diagonalization studies of correlated many-electron states in the half-filled Landau levels of graphene, including pseudospin (valley) degeneracy. We demonstrate that the polarized Fermi sea of non-interacting composite fermions remains stable against a pairing transition in the lowest two Landau levels. However, it undergoes spontaneous depolarization, which is unprotected owing to the lack of single-particle pseudospin splitting. These results suggest the absence of the Pfaffian phase in graphene.Comment: 3 pages, 4 figures (revision: reference update

Neutral Fermion Excitations in the Moore-Read state at \nu=5/2

We present evidence supporting the weakly paired Moore-Read phase in the half-filled second Landau level, focusing on some of the qualitative features of its excitations. Based on numerical studies, we show that systems with odd particle number at the flux $N_\phi=2N-3$ can be interpreted as a neutral fermion mode of one unpaired fermion, which is gapped. The mode is found to have two distinct minima, providing a signature that could be observed by photoluminescence. In the presence of two quasiparticles the same neutral fermion excitation is shown to be gapless, confirming expectations for non-Abelian statistics of the Ising model with degenerate fusion channels 1 and $\psi$.Comment: 4 pages, 4 figures; v2: final published versio

Agriculture’s inter-industry linkages, aggregation bias and rural policy reforms

As agricultural policy reform and its effects have become increasingly territorialised, analyses which attempt to explain or predict impacts need to be more localised but also identify spillover effects. In addition to the predictions of policy shocks predicted by sectoral partial equilibrium models, local and regional general equilibrium approaches which establish the wider effects of such policy shocks have become popular. However, these neglect a major, underexplored difficulty: agriculture is usually described as a single sector in input-output accounts, whereas policy shocks with differential impacts have effects on other industries which are different to those implied by average input-output coefficients. Regionalisation of aggregated input-output tables adds further to these difficulties. The objective of this paper is to develop a relatively simple method for dealing with these problems. It establishes the theoretical basis for aggregation bias and shows how it can be measured, in two contrasting case study regions in the United Kingdom and Sweden. Having established that this is a significant problem, a simple but effective procedure is demonstrated, based on additional information on variable costs, which transforms policy shocks from a direct change in agricultural output to that transmitted to the suppliers of inputs. This method provides an impact close to that which could be calculated if the general equilibrium system had indeed been disaggregated, and supports use of this approach in impact studies where the researcher does not have the time or funding available for completely disaggregating the agricultural sector’s regional accounts.agricultural and rural development policy evaluation, CAP, input-output analysis, aggregation bias, Agricultural and Food Policy,

(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves

Via the BGG correspondence a simplicial complex Delta on [n] is transformed into a complex of coherent sheaves on P^n-1. We show that this complex reduces to a coherent sheaf F exactly when the Alexander dual Delta^* is Cohen-Macaulay. We then determine when both Delta and Delta^* are Cohen-Macaulay. This corresponds to F being a locally Cohen-Macaulay sheaf. Lastly we conjecture for which range of invariants of such Delta it must be a cone.Comment: 16 pages, some minor change

Skyrmions in the Moore-Read state at nu=5/2

We study charged excitations of the non-abelian Moore-Read liquid at filling factor nu=5/2, allowing for spin depolarization. Using a combination of numerical studies, and taking account of non-zero well widths, we find that at sufficiently low Zeeman energy it is energetically favourable for charge e/4 quasiholes to bind into "skyrmions" of charge e/2. We show that skyrmion formation is further promoted by disorder, and argue that this can lead to a depolarized nu=5/2 ground state in realistic experimental situations. We comment on the consequences for the activated transport.Comment: 4 pages, 3 figure

The perils of thresholding

The thresholding of time series of activity or intensity is frequently used to define and differentiate events. This is either implicit, for example due to resolution limits, or explicit, in order to filter certain small scale physics from the supposed true asymptotic events. Thresholding the birth-death process, however, introduces a scaling region into the event size distribution, which is characterised by an exponent that is unrelated to the actual asymptote and is rather an artefact of thresholding. As a result, numerical fits of simulation data produce a range of exponents, with the true asymptote visible only in the tail of the distribution. This tail is increasingly difficult to sample as the threshold is increased. In the present case, the exponents and the spurious nature of the scaling region can be determined analytically, thus demonstrating the way in which thresholding conceals the true asymptote. The analysis also suggests a procedure for detecting the influence of the threshold by means of a data collapse involving the threshold-imposed scale.Comment: 16 pages, 10 figure

Avalanche Behavior in an Absorbing State Oslo Model

Self-organized criticality can be translated into the language of absorbing state phase transitions. Most models for which this analogy is established have been investigated for their absorbing state characteristics. In this article, we transform the self-organized critical Oslo model into an absorbing state Oslo model and analyze the avalanche behavior. We find that the resulting gap exponent, D, is consistent with its value in the self-organized critical model. For the avalanche size exponent, \tau, an analysis of the effect of the external drive and the boundary conditions is required.Comment: 4 pages, 2 figures, REVTeX 4, submitted to PRE Brief Reports; added reference and some extra information in V

Transient magnetotransport through a quantum wire

We consider an ideal parabolic quantum wire in a perpendicular magnetic field. A simple Gaussian shaped scattering potential well or hill is flashed softly on and off with its maximum at $t=0$, mimicking a temporary broadening or narrowing of the wire. By an extension of the Lippmann-Schwinger formalism to time-dependent scattering potentials we investigate the effects on the continuous current that is driven through the quantum wire with a vanishingly small forward bias. The Lippmann-Schwinger approach to the scattering process enables us to investigate the interplay between geometrical effects and effects caused by the magnetic field.Comment: RevTeX (pdf-LaTeX), 11 pages with 15 included jpg figure