Appearance of Spatial-Temporal Noise in Super-conducting Junction and Its Effect on Transport of Electron Pairs

Transport of electron pairs in super-conducting junction with spatial-temporal noise is investigated. We show that the spatial-temporal noise can produce the current of the electron pairs, which stems from a symmetry breaking of the system induced by the correlation of the spatial-temporal noise with the phase difference. It is found that there is a positive current for the electron pairs, exhibiting a peak with increasing the values of some parameters of the noises. The results provide a theoretical foundation for the further investigation of the super-conducting junction.