Attempt to describe phase slips by means of an adiabatic approximation

TL;DR

This paper investigates the limitations of using the stationary Keldysh-Usadel technique for describing phase slips in superconductors, highlighting the importance of accounting for time dependence even in slow evolution scenarios.

Contribution

It demonstrates that neglecting time variation in the stationary KUT can lead to inaccurate descriptions of phase slips, emphasizing the need for non-stationary approaches.

Findings

Neglecting time variation causes qualitative errors in phase slip description.

Stationary KUT is insufficient for slow evolution scenarios.

Non-stationary KUT provides more accurate modeling of phase slips.

Abstract

In the description of non equilibrium situations in a superconductor at temperatures far below its critical temperature, the Keldysh-Usadel technique (KUT) is required. However, the non-stationary KUT has not been applied to realistic circuits. Moreover, the stationary KUT has been applied in situations where time independence is not guaranteed. As a plausibility check for this procedure, we resort to a toy model (the Ginzburg-Landau model), in situations that involve very slow evolution. We find that, even in these situations, neglecting the explicit influence of time variation leads to inaccurate or even qualitatively wrong description of phase slips.