Consider a superconducting metal ring in which there is a persisting current $I$. I am interested in the failure of this current to remain "persisting" in the ring, although this will occur at unlikely times:
QFT says that it is possible for a vortex line to be created in the region that the ring surrounds, and then passes through the material to the other side. This will decrease the quantized flux, and upon successive such events, $I$ will drop to zero.
It is surely low, but what is the approximate rate/probability of such a process?
I would think it depends on the ring's thickness $\delta$ relative to the coherence length $\xi$ and penetration depth $\lambda$. I would also think it depends on the temperature $T$ relative to the critical temperature $T_0$, since that is the point where there is no difference between the superconductor and the normal metal.
Has this been studied in the literature? Any references are highly appreciated. (The existence of such quantum tunneling processes is known by Witten, but I don't think he studied it, and I'm guessing the analysis is either old or extremely basic.)