Mathematical model of Josephson junction

Abstract

The proposed mathematical model of the Josephson juncture allows defining the dependence of wave functions phase difference on equivalent circuit parameters. It has been shown that the solution of the differential equation, describing physical processes in the Josephson juncture may be described as power-law series, its convergence has been proved. The general equation for defining the series coefficients has been obtained. The equations for defining the wave function phase difference and Josephson juncture voltage have been obtained. The dependence of wave functions phase difference on equivalent circuit parameters and junction current has been examined.