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Non equilibrium phase diagrams of current driven Josephson junction arrays

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).