Zero-temperature resistive transition in Josephson-junction arrays at irrational frustration

We use a driven Monte Carlo dynamics in the phase representation to determine the linear resistivity and current-voltage scaling of a two-dimensional Josephson-junction array at an irrational flux quantum per plaquette. The results are consistent with a phase-coherence transition scenario where the critical temperature vanishes. The linear resistivity is nonzero at any finite temperatures but nonlinear behavior sets in at a temperature-dependent crossover current determined by the thermal critical exponent. From a dynamic scaling analysis we determine this critical exponent and the thermally activated behavior of the linear resistivity. The results are in agreement with earlier calculations using the resistively shunted-junction model for the dynamics of the array. The linear resistivity behavior is consistent with some experimental results on arrays of superconducting grains but not on wire networks, which we argue have been obtained in a current regime above the crossover current.Comment: 7 pages, 5 figures, to appear in Phys. Rev.

Fast and Slow solutions in General Relativity: The Initialization Procedure

We apply recent results in the theory of PDE, specifically in problems with two different time scales, on Einstein's equations near their Newtonian limit. The results imply a justification to Postnewtonian approximations when initialization procedures to different orders are made on the initial data. We determine up to what order initialization is needed in order to detect the contribution to the quadrupole moment due to the slow motion of a massive body as distinct from initial data contributions to fast solutions and prove that such initialization is compatible with the constraint equations. Using the results mentioned the first Postnewtonian equations and their solutions in terms of Green functions are presented in order to indicate how to proceed in calculations with this approach.Comment: 14 pages, Late

Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model

The Sinai model of a tracer diffusing in a quenched Brownian potential is a much studied problem exhibiting a logarithmically slow anomalous diffusion due to the growth of energy barriers with the system size. However, if the potential is random but periodic, the regime of anomalous diffusion crosses over to one of normal diffusion once a tracer has diffused over a few periods of the system. Here we consider a system in which the potential is given by a Brownian Bridge on a finite interval $(0,L)$ and then periodically repeated over the whole real line, and study the power spectrum $S(f)$ of the diffusive process $x(t)$ in such a potential. We show that for most of realizations of $x(t)$ in a given realization of the potential, the low-frequency behavior is $S(f) \sim {\cal A}/f^2$, i.e., the same as for standard Brownian motion, and the amplitude ${\cal A}$ is a disorder-dependent random variable with a finite support. Focusing on the statistical properties of this random variable, we determine the moments of ${\cal A}$ of arbitrary, negative or positive order $k$, and demonstrate that they exhibit a multi-fractal dependence on $k$, and a rather unusual dependence on the temperature and on the periodicity $L$, which are supported by atypical realizations of the periodic disorder. We finally show that the distribution of ${\cal A}$ has a log-normal left tail, and exhibits an essential singularity close to the right edge of the support, which is related to the Lifshitz singularity. Our findings are based both on analytic results and on extensive numerical simulations of the process $x(t)$.Comment: 8 pages, 5 figure

PROPAGATION OF BEAMS CARRYING ORBITAL ANGULAR MOMENTUM FOR DIRECTED ENERGY WEAPONS AND FREE-SPACE OPTICAL COMMUNICATIONS

This project aims to investigate the relationship between laser beams carrying orbital angular momentum (OAM) and their propagation through an optically turbulent atmosphere in the context of optical communications and directed energy weapons. These relationships and trends were determined using a custom numerical Fourier diffraction code implemented in MATLAB and using MZA’s TBWaveCalc. Vector vortex beams have been an area of interest in the optical communications community due to a proposed advantage in detection probabilities within an optically turbulent atmosphere. This thesis shows, however, that scalar vortex beams have no disadvantage over vector beams regarding detection probabilities for optical communication. For directed energy applications, higher order Laguerre-Gaussian modes, including those carrying OAM, tend to improve a directed energy weapon’s resilience to thermal blooming. This thesis investigates this behavior in the presence of turbulence. This dual study leverages traits distinct to beams carrying orbital and spin angular momentum as a means to addressing key problems in the optical communications and directed energy weapons realms.Distribution Statement A. Approved for public release: Distribution is unlimited.Ensign, United States NavyONR, Arlington, VA, 22203NPS Naval Research ProgramThis project was funded in part by the NPS Naval Research Program

Field-induced superconductor to insulator transition in Josephson-junction ladders

The superconductor to insulator transition is studied in a self-charging model for a ladder of Josephson-junctions in presence of an external magnetic field. Path integral Monte Carlo simulations of the equivalent (1+1)-dimensional classical model are used to study the phase diagram and critical behavior. In addition to a superconducting (vortex-free) phase, a vortex phase can also occur for increasing magnetic field and small charging energy. It is found that an intervening insulating phase separates the superconducting from the vortex phases. Surprisingly, a finite-size scaling analysis shows that the field-induced superconducting to insulator transition is in the KT universality class even tough the external field breaks time-reversal symmetry.Comment: 5 pages, 7 figures, to appear in Phys. Rev.