Revisiting the Langer–Ambegaokar–McCumber–Halperin theory of resistive transitions in one-dimensional superconductors with exact solutions

Abstract

We present an important correction to the Langer Ambegaokar McCumber Halperin theory for the resistive state of a 1D superconductor. We establish that the identification of the saddle on the free energy surface over which Langer and Ambegaokar had claimed the system to move in order to form thermally excited phase slip centres is wrong. With the help of an exact solution we show that the system has to overcome a similar free energy barrier but can actually have vanishing amplitude of the superconducting phase at a point, unlike the Langer-Ambegaokar solution.