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A detailed numerical study on the directed motion of ac-driven vortices and antivortices in 2D Josephson junction arrays (JJA) with an asymmetric periodic pinning potential is reported. Dc-voltage rectification shows a strong dependence on vortex density as well as an inversion of the vortex flow direction with ac amplitude for a wide range of vortex density around $f$=1/2 ($f$=$Ha^2 / \Phi_0$), in good agreement with recent experiments by Shal\'om and Pastoriza [Phys. Rev. Lett. {\bf 94}, 177001 (2005)]. The study of vortex structures, spatial and temporal correlations, and vortex-antivortex pairs formation gives insight into a purely collective mechanism behind the current reversal effect., Comment: 4 pages, 5 figures. Accepted for publication in Phys. Rev. Lett

We present a review of our numerical studies on non equilibrium vortex dynamics in Josephson Junction arrays (JJA) driven by a dc current. Dynamical phase diagrams for different magnetic fields, current directions and varying temperature are discussed and compared. First, the effect of thermal fluctuations in a current driven diluted vortex lattice (VL) with f=1/25 is analyzed. The more interesting studied regime is the one for large currents where there is sequence of transitions for the transverse response of a fast moving VL. A transverse depinning temperature below the melting transition of the moving VL is obtained. We also discuss the dependence with the direction of the applied dc current of the transport properties of diluted VL at low temperatures. We show that orientational pinning phenomenon leads to a finite transverse critical current when the bias current is applied in the directions of high symmetry and it leads to an anomalous transverse voltage when vortices are driven away from the favorable directions. In addition, the effect of disorder with a diagonal dc current applied is analyzed and a finite transverse voltage is also observed in this case. The fully frustrated JJA (f=1/2) case is also discussed. In equilibrium, the low temperature phase has two broken symmetries: the U(1) symmetry and the Z_2 symmetry. At high currents two well separated transitions are observed. The order of the checkerboard VL (discrete Z_2 symmetry) is destroyed at a much lower temperature than the transverse superconducting coherence (continuous U(1) symmetry)., Comment: 58 pages, 29 figures, Chapter contribution to "Progress in Josephson Junction Research" book, Nova Science Publishers, Inc. Ed. 2005

We study numerically the directed motion of vortices (antivortices) under an applied ac bias in two-dimensional Josephson junction arrays (JJA) with an asymmetrically modulated periodic vortex pinning potential. We find that the ratchet effect in large 2D JJA can be obtained using the RSJ model for the overdamped vortex dynamics. The rectification effect shows a strong dependence on vortex density as well as an inversion of the vortex flow direction with the ac amplitude, for a wide range of high magnetic field around f=1/2 (f being the vortex density). Our results are in good agreement with very recent experiments by D.E. Shalom and H. Pastoriza [Phys. Rev. Lett. 94, 177001, (2005)]., Comment: 4 pages, 4 figures, Proceedings Vortex IV Conference, September 3-9, 2005, Crete, Greece. To appear in Physica C

We study, analytically and numerically, phase locking of driven vortex lattices in fully-frustrated Josephson junction arrays at zero temperature. We consider the case when an ac current is applied {\it perpendicular} to a dc current. We observe phase locking, steps in the current-voltage characteristics, with a dependence on external ac-drive amplitude and frequency qualitatively different from the Shapiro steps, observed when the ac and dc currents are applied in parallel. Further, the critical current increases with increasing transverse ac-drive amplitude, while it decreases for longitudinal ac-drive. The critical current and the phase-locked current step width, increase quadratically with (small) amplitudes of the ac-drive. For larger amplitudes of the transverse ac-signal, we find windows where the critical current is hysteretic, and windows where phase locking is suppressed due to dynamical instabilities. We characterize the dynamical states around the phase-locking interference condition in the $IV$ curve with voltage noise, Lyapunov exponents and Poincar\'e sections. We find that zero temperature phase-locking behavior in large fully frustrated arrays is well described by an effective four plaquette model., Comment: 12 pages, 11 figures

We study the effect of thermal fluctuations in a fully frustrated Josephson junction array driven by a current I larger than the apparent critical current I_c(T). We calculate numerically the behavior of the chiral order parameter of Z_2 symmetry and the transverse helicity modulus (related to the U(1) symmetry) as a function of temperature. We find that the Z_2 transition occurs at a temperature T_{Z_2}(I) which is lower than the temperature T_{U(1)}(I) for the U(1) transition. Both transitions could be observed experimentally from measurements of the longitudinal and transverse voltages., Comment: 4 pages, 4 figures

We study the non-equilibrium dynamical regimes of a moving vortex lattice in the periodic pinning of a Josephson junction array (JJA) for {\it finite temperatures} in the case of a fractional or submatching field. We obtain a phase diagram for the current driven JJA as a function of the driving current I and temperature T. We find that when the vortex lattice is driven by a current, the depinning transition at $T_p(I)$ and the melting transition at $T_M(I)$ become separated even for a field for which they coincide in equilibrium. We also distinguish between the depinning of the vortex lattice in the direction of the current drive, and the {\it transverse depinning} in the direction perpendicular to the drive. The transverse depinning corresponds to the onset of transverse resistance in a moving vortex lattice at a given temperature $T_{tr}$. For driving currents above the critical current we find that the moving vortex lattice has first a transverse depinning transition at low T, and later a melting transition at a higher temperature, $T_{M}>T_{tr}$., Comment: 17 pages, 19 figures

We study the effect of thermal fluctuations in a vortex lattice driven in the periodic pinning of a Josephson junction array. The phase diagram current ($I$) vs. temperature ($T$) is studied. Above the critical current $I_c(T)$ we find a moving vortex lattice (MVL) with anisotropic Bragg peaks. For large currents $I\gg I_c(T)$, there is a melting transition of the MVL at $T_M(I)$. When applying a small transverse current to the MVL, there is no dissipation at low $T$. We find an onset of transverse vortex motion at a transverse depinning temperature $T_{tr}(I)