  The magneto-conductance in YBCO grain boundary Josephson junctions, displays
fluctuations at low temperatures of mesoscopic origin. The morphology of the
junction suggests that transport occurs in narrow channels across the grain
boundary line, with a large Thouless energy. Nevertheless the measured
fluctuation amplitude decreases quite slowly when increasing the voltage up to
values about twenty times the Thouless energy, of the order of the nominal
superconducting gap. Our findings show the coexistence of supercurrent and
quasiparticle current in the junction conduction even at high nonequilibrium
conditions. Model calculations confirm the reduced role of quasiparticle
relaxation at temperatures up to 3 Kelvin.
