Semiclassical treatment of the path-integral approach to special effects in superconductivity

Abstract Distinctive features of the flux mode regime in the Anderson-Josephson potential are analyzed using both semiclassical path-integral and instanton techniques. This potential governs the behavior of a superconducting ring interrupted by a weak Josephson junction. After establishing the relation between WKB and functional-integral approximations, semiclassical expansions are derived from a discretized version of the Feynman propagator. The physical meaning of instantons is extended to the condensed matter problem of “energy spectrum” for weak-link ring states localized near the minimum energy regions. Under certain circumstances, an improved WKB approximation enables us to find expression for the decay rates of metastable states, performing the reduction of the original Anderson-Josephson shape to a double-hump structure. Although we have not discussed here the temperature dependence of the Josephson plasma frequency, our calculations are consistent with recent theories for systems at finite temperatures with two metastable states separated by a potential energy barrier.