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Dissipation mechanism above the current threshold in Josephson junction chains

We present measurements on one-dimensional Josephson junction arrays formed by a chain of SQUID loops in the regime where $E_J / E_c\simeq 1$. We observe a blockaded zero current branch for small bias voltages. Above a certain voltage $V_\mathrm{sw}$ the $I$-$V$ characteristics changes discontinuously to a dissipative branch characterized by a flux dependent conductance. Three of four samples show a pronounced hysteresis for a forward and backward voltage sweep. We observe a periodic field dependence of the conductance above $V_\mathrm{sw}$ which can be described with $P(E)$ theory for cooper-pairs and therefore gives evidence of viscous dynamics of Cooper pair transport through the array.