PHYSICAL BASIS FOR HALF-INTEGRAL SHAPIRO STEPS IN A DC SQUID

The dynamics of a DC SQUID is analogous to the classical dynamics of a particle subject to conservative, damping, and driving forces in two dimensions. The equations of motion define a trajectory on a potential-energy surface derived from the conservative forces, the components of which correspond to different forms of stored energy in the SQUID, In the presence of a periodic driving force, half-integral Shapiro steps are possible when the trajectory follows a zig-zag path between minima of the potential surface. This description of the dynamics in terms of a potential surface provides an intuitive, physical basis for previous simulation results on half-integral Shapiro steps in a DC SQUID.