Superfluid flow past an array of scatterers

We consider a model of nonlinear superfluid flow past a periodic array of pointlike scatterers in one dimension. We find a rich dependence of the critical current on both the scatterer strength and separation. In particular, in the case of attractive impurities, we find the critical current at any separation to vanish entirely at some critical scatterer strength. An experimental application of this model is in the critical current of a Josephson array in a regime appropriate to a Ginzburg-Landau formulation. The above results translate to the critical current of the array depending linearly as A(T-c- T), when the temperature T is close to the critical temperature T-c. Here the coefficient A depends sensitively on the array geometry and the strength and sign of the Hartree interaction in the normal regions. Furthermore, in the case of an attractive interaction, the critical current will vanish linearly at some temperature T* less than T-c, as well as at T-c itself. We examine the origin of a zero critical current at a critical scatterer strength, ruling out a simple explanation in terms of sound wave radiation at low frequencies. Instead we suggest an interpretation in terms of a nonlinear mapping from the Ginzburg-Landau equation to the sine-Gordon equation. [S0163-1829(99)13541-0].