Boundary Effects on Dynamic Behavior of Josephson-Junction Arrays

The boundary effects on the current-voltage characteristics in two-dimensional arrays of resistively shunted Josephson junctions are examined. In particular, we consider both the conventional boundary conditions (CBC) and the fluctuating twist boundary conditions (FTBC), and make comparison of the obtained results. It is observed that the CBC, which have been widely adopted in existing simulations, may give a problem in scaling, arising from rather large boundary effects; the FTBC in general turn out to be effective in reducing the finite-size effects, yielding results with good scaling behavior. To resolve the discrepancy between the two boundary conditions, we propose that the proper scaling in the CBC should be performed with the boundary data discarded: This is shown to give results which indeed scale well and are the same as those from the FTBC.Comment: RevTex, Final version to appear in Phys. Rev.

Ubiquitous finite-size scaling features in IV characteristics of various dynamic XY models in two dimensions

Two-dimensional (2D) XY model subject to three different types of dynamics, namely Monte Carlo, resistivity shunted junction (RSJ), and relaxational dynamics, is numerically simulated. From the comparisons of the current-voltage (I-V) characteristics, it is found that up to some constants I-V curves at a given temperature are identical to each other in a broad range of external currents. Simulations of the Villain model and the modified 2D XY model allowing stronger thermal vortex fluctuations are also performed with RSJ type of dynamics. The finite-size scaling suggested in Medvedyeva et al. [Phys. Rev. B 62, 14531(2000)] is confirmed for all dynamic models used, implying that this finite-size scaling behaviors in the vicinity of the Kosterlitz-Thouless transition are quite robust.Comment: 7 pages, 4 pictures, accepted in Physica

Splitting of the superconducting transition in the two weakly coupled 2D XY models

The frequency $\omega$ and temperature T dependent complex conductivity $\sigma$ of two weakly coupled 2D XY models subject to the RSJ dynamics is studied through computer simulations. A double dissipation-peak structure in $Re[\omega\sigma]$ is found as a function of T for a fixed frequency. The characteristics of this double-peak structure, as well as its frequency dependence, is investigated with respect to the difference in the critical temperatures of the two XY models, originating from their different coupling strengths. The similarity with the experimental data in Festin {\it et al.} [Physica C 369, 295 (2002)] for a thin YBCO film is pointed out and some possible implications are suggested.Comment: 4 pages, 4 figure

Phase Transition in the Two Dimensional Classical XY Model

For the two dimensional classical XY model we present extensive high -temperature -phase bulk data extracted based on a novel finite size scaling (FSS) Monte Carlo technique, along with FSS data near criticality. Our data verify that $\eta=1/4$ sets in near criticality, and clarify the nature of correction to the leading scaling behavior. However, the result of standard FSS analysis near criticality is inconsistent with other predictions of Kosterlitz's renormalization group approach.Comment: Significant changes in the text and the figures. To appear in Phys. Lett. A Hard copies of seven figures are available upon reques

Current-voltage characteristics of the two-dimensional XY model with Monte Carlo dynamics

Current-voltage characteristics and the linear resistance of the two-dimensional XY model with and without external uniform current driving are studied by Monte Carlo simulations. We apply the standard finite-size scaling analysis to get the dynamic critical exponent $z$ at various temperatures. From the comparison with the resistively-shunted junction dynamics, it is concluded that $z$ is universal in the sense that it does not depend on details of dynamics. This comparison also leads to the quantification of the time in the Monte Carlo dynamic simulation.Comment: 5 pages in two columns including 5 figures, to appear in PR

Extraction of the pion-nucleon sigma-term from the spectrum of exotic baryons

The pion nucleon sigma-term is extracted on the basis of the soliton picture of the nucleon from the mass spectrum of usual and the recently observed exotic baryons, assuming that they have positive parity. The value found is consistent with that inferred by means of conventional methods from pion nucleon scattering data. The study can also be considered as a phenomenological consistency check of the soliton picture of baryons.Comment: 8 pages, 2 figures, references added, discussion extended, to appear in Eur.Phys.J.

Explicit Chabauty-Kim theory for the thrice punctured line in depth two

Let $X= \mathbb{P}^1 \setminus \{0,1,\infty\}$, and let $S$ denote a finite set of prime numbers. In an article of 2005, Minhyong Kim gave a new proof of Siegel's theorem for $X$: the set $X(\mathbb{Z}[S^{-1}])$ of $S$-integral points of $X$ is finite. The proof relies on a `nonabelian' version of the classical Chabauty method. At its heart is a modular interpretation of unipotent $p$-adic Hodge theory, given by a tower of morphisms $h_n$ between certain $\mathbb{Q}_p$-varieties. We set out to obtain a better understanding of $h_2$. Its mysterious piece is a polynomial in $2|S|$ variables. Our main theorem states that this polynomial is quadratic, and gives a procedure for writing its coefficients in terms of $p$-adic logarithms and dilogarithms.Comment: The appendix has been removed and posted as a separate preprint. Some detail added to our sketch of the construction of the "unipotent p-adic Hodge morphism" $h_n$ in the introduction. Technical errors corrected in Sections 3 and 4. Minor corrections and improvements throughou

Magnetic-field dependence of dynamical vortex response in two-dimensional Josephson junction arrays and superconducting films

The dynamical vortex response of a two-dimensional array of the resistively shunted Josephson junctions in a perpendicular magnetic field is inferred from simulations. It is found that, as the magnetic field is increased at a fixed temperature, the response crosses over from normal to anomalous, and that this crossover can be characterized by a single dimensionless parameter. It is described how this crossover should be reflected in measurements of the complex impedance for Josephson junction arrays and superconducting films.Comment: 4 pages including 5 figures in two columns, final versio