Local dynamic behaviors of long 0-π Josephson junction

Abstract

The mathematical discontinuity existing in the phase-difference dynamic model for the Josephson junction results in the challenge of the dynamic analysis on the Josephson junction. Focusing on the non-smooth characteristics of the dynamic model for the long 0-π Josephson junction, two typical local dynamic behaviors, including the moving breather and the semifluxon interaction, are investigated by the structure-preserving approach based on the multi-symplectic idea in this paper. Firstly, the symmetric form with two segmented local conservation laws is derived form the non-smooth sine-Gordon-type model controlling the evolution of the phase-difference in the long 0-π Josephson junction. And then, the numerical experiments on the above local dynamic behaviors are performed using the proposed structure-preserving approach. The novel discoveries on the local dynamic behaviors of the long 0-π Josephson junction include: The non-dissipative characteristic of the moving breather that revises the widely accepted conclusion on the dissipative characteristic of the moving breather, and the asymmetric phase jumps for the pinned semifluxons that can be used to comprehend the anharmonic supercurrent in the Josephson junction. The above findings on the local dynamic behaviors of the long 0-π Josephson junction will give some guidance on the design of digital single flux quantum circuits.