Feynman's and Ohta's models of a Josephson junction (Q2867193)

The paper studies the difference between Feynman's and Ohta's models for a Josephson junction (JJ). It is shown that the Feynman's model can be considered as a specific description of a weakly coupled two-level quantum system which does not provide a consistent account of the external bias circuit. Due to the voltage-frequency Josephson relation does not appear in its strict form. For this, there are considered two weakly coupled superconductors forming a JJ and dynamics of the system described by the Schrödinger equation. As a result, it is shown for the strict voltage-frequency Josephson relation, the conservation of charge violates in the Feynman's model. Then the author considers in a simplified version the reasoning adopted by Ohta taking into account the extra term due to presence of an external classical circuit. Based on quantum mechanical considerations, the classically observable energy is considered by using the classical complete Hamiltonian. As a result, the obtained condition gives the strict voltage-frequency relation and then the phase-current relation. Based on these two analyses (quantum mechanical and semi-classical) De Luca and Romeo have before derived the correct dynamical equations for a double-barrier JJ (DBJJ) with a thin intermediate electrode. Extension of this approach to multilayered systems is finally mentioned in this paper. In particular, based on the Ohta's picture, a tri-layer system can be viewed as a modified JJ in which the interstitial subsystem consisting of a thin superconducting region can be treated as a pure quantum system.