Microscopic theory of thermal phase slips in clean narrow superconducting wires

We consider the structure of a thermal phase-slip center for a simple microscopic model of a clean one-dimensional superconductor in which superconductivity occurs only within one conducting channel or several identical channels. Surprisingly, the Eilenberger equations describing the saddle-point configuration allow for an exact analytical solution in the whole temperature and current range. This solution allows us to derive a closed expression for the free-energy barrier, which we use to compute its temperature and current dependences.