Nielsen Identity and the Renormalization Group Functions in an Abelian Supersymmetric Chern-Simons Model in the Superfield Formalism

In this paper we study the Nielsen identity for the supersymmetric Chern-Simons-matter model in the superfield formalism, in three spacetime dimensions. The Nielsen identity is essential to understand the gauge invariance of the symmetry breaking mechanism, and it is calculated by using the BRST invariance of the model. We discuss the technical difficulties in applying this identity to the complete effective superpotential, but we show how we can study in detail the gauge independence of one part of the effective superpotential, $K_{eff}$. We calculate the renormalization group functions of the model for arbitrary gauge-fixing parameter, finding them to be independent of the gauge choice. This result can be used to argue that $K_{eff}$ also does not depend on the gauge parameter. We discuss the possibility of the extension of these results to the complete effective superpotential.Comment: v2: 23 pages, 4 figures, version accepted for publication in PR

Regularity of quasi-stationary measures for simple exclusion in dimension d >= 5

We consider the symmetric simple exclusion process on Z^d, for d>= 5, and study the regularity of the quasi-stationary measures of the dynamics conditionned on not occupying the origin. For each \rho\in ]0,1[, we establish uniqueness of the density of quasi-stationary measures in L^2(d\nur), where \nur is the stationary measure of density \rho. This, in turn, permits us to obtain sharp estimates for P_{\nur}(\tau>t), where \tau is the first time the origin is occupied.Comment: 18 pages. Corrections after referee report. To be published in Ann Proba

Anisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure

In [arXiv:0804.3035] we studied an interacting particle system which can be also interpreted as a stochastic growth model. This model belongs to the anisotropic KPZ class in 2+1 dimensions. In this paper we present the results that are relevant from the perspective of stochastic growth models, in particular: (a) the surface fluctuations are asymptotically Gaussian on a sqrt(ln(t)) scale and (b) the correlation structure of the surface is asymptotically given by the massless field.Comment: 13 pages, 4 figure

Hitting times for independent random walks on Zd\mathbb{Z}^d

We consider a system of asymmetric independent random walks on $\mathbb{Z}^d$, denoted by $\{\eta_t,t\in{\mathbb{R}}\}$, stationary under the product Poisson measure $\nu_{\rho}$ of marginal density $\rho>0$. We fix a pattern $\mathcal{A}$, an increasing local event, and denote by $\tau$ the hitting time of $\mathcal{A}$. By using a loss network representation of our system, at small density, we obtain a coupling between the laws of $\eta_t$ conditioned on $\{\tau>t\}$ for all times $t$. When $d\ge3$, this provides bounds on the rate of convergence of the law of $\eta_t$ conditioned on $\{\tau>t\}$ toward its limiting probability measure as $t$ tends to infinity. We also treat the case where the initial measure is close to $\nu_{\rho}$ without being product.Comment: Published at http://dx.doi.org/10.1214/009117906000000106 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Poisson approximation for large-contours in low-temperature Ising models

We consider the contour representation of the infinite volume Ising model at low temperature. Fix a subset V of Z^d, and a (large) N such that calling G_{N,V} the set of contours of length at least N intersecting V, there are in average one contour in G_{N,V} under the infinite volume "plus" measure. We find bounds on the total variation distance between the law of the contours of lenght at least N intersecting V under the "plus" measure and a Poisson process. The proof builds on the Chen-Stein method as presented by Arratia, Goldstein and Gordon. The control of the correlations is obtained through the loss-network space-time representation of contours due to Fernandez, Ferrari and Garcia.Comment: 10 pages, to appear in Physica

Raman Fingerprint of Charged Impurities in Graphene

We report strong variations in the Raman spectra for different single-layer graphene samples obtained by micromechanical cleavage, which reveals the presence of excess charges, even in the absence of intentional doping. Doping concentrations up to ~10^13 cm-2 are estimated from the G peak shift and width, and the variation of both position and relative intensity of the second order 2D peak. Asymmetric G peaks indicate charge inhomogeneity on the scale of less than 1 micron.Comment: 3 pages, 5 figure

Dynamical and radiative properties of astrophysical supersonic jets I. Cocoon morphologies

We present the results of a numerical analysis of the propagation and interaction of a supersonic jet with the external medium. We discuss the motion of the head of the jet into the ambient in different physical conditions, carrying out calculations with different Mach numbers and density ratios of the jet to the exteriors. Performing the calculation in a reference frame in motion with the jet head, we can follow in detail its long term dynamics. This numerical scheme allows us also to study the morphology of the cocoon for different physical parameters. We find that the propagation velocity of the jet head into the ambient medium strongly influences the morphology of the cocoon, and this result can be relevant in connection to the origin and structure of lobes in extragalactic radiosources.Comment: 14 pages, TeX. Accepted for A&

How to squeeze the toothpaste back into the tube

We consider "bridges" for the simple exclusion process on Z, either symmetric or asymmetric, in which particles jump to the right at rate p and to the left at rate 1-p. The initial state O has all negative sites occupied and all non-negative sites empty. We study the probability that the process is again in state O at time t, and the behaviour of the process on [0,t] conditioned on being in state O at time t. In the case p=1/2, we find that such a bridge typically goes a distance of order t (in the sense of graph distance) from the initial state. For the asymmetric systems, we note an interesting duality which shows that bridges with parameters p and 1-p have the same distribution; the maximal distance of the process from the original state behaves like c(p)log(t) for some constant c(p) depending on p. (For p>1/2, the front particle therefore travels much less far than the bridge of the corresponding random walk, even though in the unconditioned process the path of the front particle dominates a random walk.) We mention various further questions.Comment: 15 page