Critical currents for vortex defect motion in superconducting arrays

We study numerically the motion of vortices in two-dimensional arrays of resistively shunted Josephson junctions. An extra vortex is created in the ground states by introducing novel boundary conditions and made mobile by applying external currents. We then measure critical currents and the corresponding pinning energy barriers to vortex motion, which in the unfrustrated case agree well with previous theoretical and experimental findings. In the fully frustrated case our results also give good agreement with experimental ones, in sharp contrast with the existing theoretical prediction. A physical explanation is provided in relation with the vortex motion observed in simulations.Comment: To appear in Physical Review

Dynamic transition and Shapiro-step melting in a frustrated Josephson-junction array

We consider a two-dimensional fully frustrated Josephson-junction array driven by combined direct and alternating currents. Interplay between the mode locking phenomenon, manifested by giant Shapiro steps in the current-voltage characteristics, and the dynamic phase transition is investigated at finite temperatures. Melting of Shapiro steps due to thermal fluctuations is shown to be accompanied by the dynamic phase transition, the universality class of which is also discussed

Spatiotemporal Stochastic Resonance in Fully Frustrated Josephson Ladders

We consider a Josephson-junction ladder in an external magnetic field with half flux quantum per plaquette. When driven by external currents, periodic in time and staggered in space, such a fully frustrated system is found to display spatiotemporal stochastic resonance under the influence of thermal noise. Such resonance behavior is investigated both numerically and analytically, which reveals significant effects of anisotropy and yields rich physics.Comment: 8 pages in two columns, 8 figures, to appear in Phys. Rev.

Counting statistics based on the analytic solutions of the differential-difference equation for birth-death processes

Birth-death processes take place ubiquitously throughout the universe. In general, birth and death rates depend on the system size (corresponding to the number of products or customers undergoing the birth-death process) and thus vary every time birth or death occurs, which makes fluctuations in the rates inevitable. The differential-difference equation governing the time evolution of such a birth-death process is well established, but it resists solving for a non-asymptotic solution. In this work, we present the analytic solution of the differential-difference equation for birth-death processes without approximation. The time-dependent solution we obtain leads to an analytical expression for counting statistics of products (or customers). We further examine the relationship between the system size fluctuations and the birth and death rates, and find that statistical properties (variance subtracted by mean) of the system size are determined by the mean death rate as well as the covariance of the system size and the net growth rate (i.e., the birth rate minus the death rate). This work suggests a promising new direction for quantitative investigations into birth-death processes