Dynamics of emergent Cooper pairing at finite temperatures

TL;DR

This paper investigates how fermionic systems with pairing interactions evolve over time at finite temperatures after a sudden increase in coupling, revealing temperature-dependent damped oscillations in the order parameter.

Contribution

It provides a detailed analysis of the finite-temperature dynamics of Cooper pairing, highlighting differences based on initial phases and identifying key parameters affecting decay times.

Findings

Normal phase initial states show damped oscillations in the order parameter.

Decay times depend on temperature, level spacing, and initial BCS gap.

Superfluid initial states exhibit negligible decay after coupling increase.

Abstract

We study the time evolution of a system of fermions with pairing interactions at a finite temperature. The dynamics is triggered by an abrupt increase of the BCS coupling constant. We show that if initially the fermions are in a normal phase, the amplitude of the BCS order parameter averaged over the Boltzman distribution of initial states exhibits damped oscillations with a relatively short decay time. The latter is determined by the temperature, the single-particle level spacing, and the ground state value of the BCS gap for the new coupling. In contrast, the decay is essentially absent when the system was in a superfluid phase before the coupling increase.