Rung-Rung Current Correlations on a 2-Leg t-J Ladder

We report the results of numerical calculations of rung-rung current correlations on a 2-leg t-J ladder with J/t=0.35 for dopings x=0.125 and x=0.19. We find that the amplitude of these correlations decays exponentially. We argue that this can be understood within a bosonization framework in terms of the pinned phase variables associated with a C1SO phase with d_{x^2-y^2}-like power law pairing correlations.