We study thermal phase slips in an infinite 2D superconducting film within the Usadel model. Recently, the free-energy instanton was obtained in the Ginzburg–Landau region in the vicinity of the critical current. The proximity to the critical current allows one to reduce the Ginzburg–Landau equations to the exactly integrable Boussinesq equation [1]. Using the scaling of the instanton parameters obtained in [1], we perform a gradient expansion of the Usadel equations near the critical current. Keeping only the leading terms in the free energy functional, we transform it into the Boussinesq form and find the activation barrier at arbitrary temperatures using the known instanton profile. In the 1D geometry, our approach yields the asymptotics of the barrier near the critical current, consistent with numerical results from [2].

[1] M. A. Skvortsov and A. V. Polkin, arXiv:2506.18130.
[2] A. V. Semenov, P. A. Krutitskii and I. A. Devyatov, Jetp Lett. 92, 762 (2010)

We study the behavior of hydrodynamic modes in dissipative fermion systems with a conserved number of particles. The model under consideration describes a class of fermion systems with a symmetric two-band spectrum, a conserved number of particles, and energy and momentum dissipation due to interaction with a boson bath. The evolution of the density matrix of such a system can be described using the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) equation or, equivalently, in terms of Keldysh field theory. In previous papers on this topic, we studied the system's dynamics using diagrammatic techniques within the Keldysh functional integral formalism. It turned out that the fermion dynamics are described by a system of two coupled equations for the densities in the upper and lower bands, which have the form of the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation. In this work, we continue the theme using field theory methods: in the Keldysh action, we can clearly distinguish hydrodynamic and massive modes that describe the dynamics of deviations from the saddle-point approximation. Averaging over the massive modes reduces the hydrodynamic action to the familiar FKPP equations and allows us to use the renormalization group method to determine whether previously obtained results are tied to a small dissipation coefficient, as well as whether the model exhibits a phase transition with respect to this parameter. This work was carried out within the framework of state assignment FFWR-2024-0017.