Field theoretic model for the Josephson effect

Abstract

The Josephson effect is found to stem from the quantum behavior of massive photons existing in a superconducting medium. Accordingly, the Josephson coupling energy is found to be equal to the rest mass energy of these photons. The Josephson effect is described by propagation of massive photon field following the universal quantum equation instead of being due to quantum tunnelling. The mass of the photon is found to be dependent on the electric properties of the junction. A characteristic (critical) quantized capacitance of the junction is found to be inversely related to the critical current. The quantum (kinetic) inductance induced in the junction is found to be equal to $L_q=\mu_0\lambda_J$\,, where $\lambda_J$ is the Josephson penetration depth, and $\mu_0$ is the free space permeability.