Classical Dynamics of Josephson Tunnelling and Its Quantum Limitations

Abstract

In the dynamics of Josephson tunnel junctions the quantum phase shift of the superconducting order parameter is the important degree of freedom. The highly non-linear stationary response to external excitations and the resistivity associated with the transport of superconducting current carriers through the junction under non-stationary conditions make the Josephson junction a favoured object for fundamental physical questions and for important quantum electronic applications as well. This article is intended to present a comprehensive description of the classical dynamics of the quantum phase shift occurring in superconducting Josephson tunnel junctions in the framework of linear response theory. This description is equivalent to the Kubo formalism known from irreversible thermodynamics. Firstly, it allows the dynamical properties of all kinds of superconductors to be emphasized, connected by tunnel junctions. Secondly, it permits an equivalent circuit of the junction to be set up. This quantum network description turns out to be extremely useful for modelling, simulating, and designing superconducting electronic circuits (cf. article by G. BRUNK). The quantum limitations of the classical Josephson effect will be discussed and the present state of macroscopic quantum phenomena will be indicated.