Josephson-junction threshold viewed as a critical point

We examine the expression for the mean thermal-noise voltage in the dc Josephson effect obtained by Ambegaokar and Halperin via a Brownian-motion analogy. We find that their expression can be reduced to closed form by two different methods which give the same result. This exact closed-form expression is used to derive analytic approximations in several limits and we find that the behavior of the mean voltage near the threshold current is characterized by "critical exponents" which bear a remarkable resemblance to those exhibited by an order parameter near the critical point of a continuous phase transition.