%0 Journal Article %T Nucleation and Growth of the Superconducting Phase in the Presence of a Current %A Andrew J. Dolgert %A Thomas Blum %A Alan T. Dorsey %A Michael Fowler %J Physics %D 1997 %I arXiv %R 10.1103/PhysRevB.57.5432 %X We study the localized stationary solutions of the one-dimensional time-dependent Ginzburg-Landau equations in the presence of a current. These threshold perturbations separate undercritical perturbations which return to the normal phase from overcritical perturbations which lead to the superconducting phase. Careful numerical work in the small-current limit shows that the amplitude of these solutions is exponentially small in the current; we provide an approximate analysis which captures this behavior. As the current is increased toward the stall current J*, the width of these solutions diverges resulting in widely separated normal-superconducting interfaces. We map out numerically the dependence of J* on u (a parameter characterizing the material) and use asymptotic analysis to derive the behaviors for large u (J* ~ u^-1/4) and small u (J -> J_c, the critical deparing current), which agree with the numerical work in these regimes. For currents other than J* the interface moves, and in this case we study the interface velocity as a function of u and J. We find that the velocities are bounded both as J -> 0 and as J -> J_c, contrary to previous claims. %U http://arxiv.org/abs/cond-mat/9709125v1