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

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

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

Experimental manifestation of the breakpoint region in the current-voltage characteristics of intrinsic Josephson junctions

The experimental evidence of the breakpoint on the current-voltage characteristics (IVCs) of the stacks of intrinsic Josephson junctions (IJJs) is presented. The influence of the capacitive coupling on the IVCs of Bi$_2$Sr$_2$CaCu$_2$O$_y$ IJJs has been investigated. At 4.2 K, clear breakpoint region is observed on the branches in the IVCs. It is found that the hysteresis observed on the IVC is suppressed due to the coupling compared with that expected from the McCumber parameter. Measurements agree well with the results obtained by the theoretical model.Comment: 3 pages, 4 figure