On Wilson Criterion

U(1) gauge theory with the Villain action on a cubic lattice approximation of three- and four-dimensional torus is considered. The naturally chosen correlation functions converge to the correlation functions of the R-gauge electrodynamics on three- and four-dimensional torus as the lattice spacing approaches zero only for the special scaling. This special scaling depends on a choice of a correlation function system. Another scalings give the degenerate continuum limits. The Wilson criterion for the confinement is ambiguous. The asymptotics of the smeared Wilson loop integral for the large loop perimeters is defined by the density of the loop smearing over a torus which is transversal to the loop plane. When the initial torus radius tends to infinity the correlation functions converge to the correlation functions of the R-gauge Euclidean electrodynamics.Comment: latex, 6 page

Semiparametric estimation for a class of time-inhomogenous diffusion processes

Copyright @ 2009 Institute of Statistical Science, Academia SinicaWe develop two likelihood-based approaches to semiparametrically estimate a class of time-inhomogeneous diffusion processes: log penalized splines (P-splines) and the local log-linear method. Positive volatility is naturally embedded and this positivity is not guaranteed in most existing diffusion models. We investigate different smoothing parameter selections. Separate bandwidths are used for drift and volatility estimation. In the log P-splines approach, different smoothness for different time varying coefficients is feasible by assigning different penalty parameters. We also provide theorems for both approaches and report statistical inference results. Finally, we present a case study using the weekly three-month Treasury bill data from 1954 to 2004. We find that the log P-splines approach seems to capture the volatility dip in mid-1960s the best. We also present an application to calculate a financial market risk measure called Value at Risk (VaR) using statistical estimates from log P-splines

Depairing currents in superconducting films of Nb and amorphous MoGe

We report on measuring the depairing current J_{dp} in thin superconducting films as a function of temperature. The main difficulties in such measurements are that heating has to be avoided, either due to contacts, or to vortex flow. The latter is almost unavoidable since the sample cross-section is usually larger than the superconducting coherence length \xi_s and the magnetic field penetration depth \lambda_s. On the other hand, vortex flow is helpful since it homogenizes the distribution of the current across the sample. We used a pulsed current method, which allows to overcome the difficulties caused by dissipation and measured the depairing current in films of thin polycrystalline Nb (low \lambda_s, low specific resistance \rho) and amorphous Mo_{0.7}Ge_{0.3} (high \lambda_s, high \rho), structured in the shape of bridges of various width. The experimental values of J_{dp} for different bridge dimensions are compared with theoretical predictions by Kupriyanov and Lukichev for dirty limit superconductors. For the smallest samples we find a very good agreement with theory, over essentially the whole temperature interval below the superconducting critical temperature.Comment: 5 pages, 6 figure

Supercurrent fluctuations in short filaments

We evaluate the average and the standard deviation of the supercurrent in superconducting nanobridges, as functions of the temperature and the phase difference, in an equilibrium situation. We also evaluate the autocorrelation of the supercurrent as a function of the elapsed time. The behavior of supercurrent fluctuations is qualitatively different from from that of the normal current: they depend on the phase difference, have a different temperature dependence, and for appropriate range their standard deviation is independent of the probing time. We considered two radically different filaments and obtained very similar results for both. Fluctuations of the supercurrent can in principle be measured

Local linear spatial quantile regression

Copyright @ 2009 International Statistical Institute / Bernoulli Society for Mathematical Statistics and Probability.Let {(Yi,Xi), i ∈ ZN} be a stationary real-valued (d + 1)-dimensional spatial processes. Denote by x → qp(x), p ∈ (0, 1), x ∈ Rd , the spatial quantile regression function of order p, characterized by P{Yi ≤ qp(x)|Xi = x} = p. Assume that the process has been observed over an N-dimensional rectangular domain of the form In := {i = (i1, . . . , iN) ∈ ZN|1 ≤ ik ≤ nk, k = 1, . . . , N}, with n = (n1, . . . , nN) ∈ ZN. We propose a local linear estimator of qp. That estimator extends to random fields with unspecified and possibly highly complex spatial dependence structure, the quantile regression methods considered in the context of independent samples or time series. Under mild regularity assumptions, we obtain a Bahadur representation for the estimators of qp and its first-order derivatives, from which we establish consistency and asymptotic normality. The spatial process is assumed to satisfy general mixing conditions, generalizing classical time series mixing concepts. The size of the rectangular domain In is allowed to tend to infinity at different rates depending on the direction in ZN (non-isotropic asymptotics). The method provides muchAustralian Research Counci

Stationary Charge Imbalance Effect in System of Coupled Josephson Junction

We investigate stationary charge imbalance effect in the system of coupled overdamped Josephson junctions. We show that coupling between junction and nonzero stationary charge imbalance in the resistive state bring to a decrease of the Josephson frequency in the Josephson junctions of the stack. The formed difference in Josephson frequency leads to the nonuniform switch to the Shapiro step regime in the presence of external electromagnetic radiation and appearance of kinks of voltage on the IV-characteristics of the stack. We also show that stationary charge imbalance brings to the slope of the Shapiro step due to the difference of the charge imbalance potential on the edges of the step. The theoretical and experimental results for voltage bias coupled Josephson junctions have been compared with the current bias case