Condition of the occurrence of phase slip centers in superconducting nanowires under applied current or voltage

Experimental results on the phase slip process in superconducting lead nanowires are presented under two different experimental conditions: constant applied current or constant voltage. Based on these experiments we established a simple model which gives us the condition of the appearance of phase slip centers in a quasi-one-dimensional wire. It turns out that the competition between two relaxations times (relaxation time of the absolute value of the order parameter $\tau_{|\psi|}$ and relaxation time of the phase of the order parameter in the phase slip center $\tau_{\phi}$) governs the phase slip process. Phase slip phenomena, as periodic oscillations in time of the order parameter, is possible only if the gradient of the phase grows faster than the value of the order parameter in the phase slip center, or equivalently if $\tau_{\phi}<\tau_{|\psi|}$.