Nonequilibrium relaxation in neutral BCS superconductors: Ginzburg-Landau approach with Landau damping in real time

TL;DR

This paper develops a real-time, field-theoretical approach to study the nonequilibrium relaxation dynamics of order parameter fluctuations in neutral BCS superconductors, incorporating Landau damping effects.

Contribution

It introduces a consistent real-time method to derive equations of motion for fluctuations, including Landau damping, near the critical point in BCS superconductors.

Findings

Phase fluctuations are overdamped by Landau damping.

Relaxation time diverges at the critical point, indicating critical slowing down.

The effective action becomes nonlocal due to Landau damping.

Abstract

We present a field-theoretical method to obtain consistently the equations of motion for small amplitude fluctuations of the order parameter directly in real time for a homogeneous, neutral BCS superconductor. This method allows to study the nonequilibrium relaxation of the order parameter as an initial value problem. We obtain the Ward identities and the effective actions for small phase the amplitude fluctuations to one-loop order. Focusing on the long-wavelength, low-frequency limit near the critical point, we obtain the time-dependent Ginzburg-Landau effective action to one-loop order, which is nonlocal as a consequence of Landau damping. The nonequilibrium relaxation of the phase and amplitude fluctuations is studied directly in real time. The long-wavelength phase fluctuation (Bogoliubov-Anderson-Goldstone mode) is overdamped by Landau damping and the relaxation time scale diverges at the critical point, revealing critical slowing down.