Spectral Flow in Josephson Junctions and Effective Magnus Force

Momentum production during the phase slip process in SNS Josephson junction is discussed. It is caused by the spectral flow of bound states of fermions localized within the junction. This effectively reduces the Magnus force acting on vortices which provides an explanation for the experimental observation of the negligible Magnus force in 2D Josephson junction arrays. The flow of the fermionic levels is similar to that in sphalerons in particle physics, where it gives rise to the baryogenesis.