Intrinsic Fluctuations in Superconducting Rings Containing One-Dimensional Weak Links

The Langer-Ambegaokar statistical theory of dissipative fluctuations in narrow superconducting channels is extended to describe the quantum transitions of a closed superconducting ring containing a long one-dimensional weak-link section. The external magnetic flux ${\Phi }_e$ linking the loop is the independent thermo-dynamic variable. Based upon the Ginzburg-Landau free energy, the theory is expected to accurately describe single-quantum transitions for $T$ near but slightly below $T_c$. Data reported by Lukens and Good-kind for thin-film Sn rings are reasonably consistent with the theory, but more definitive experimental tests are required.