Dynamical Selection in Emergent Fermionic Pairing

TL;DR

This paper investigates the time evolution of a Fermi gas under a dynamic BCS interaction, revealing that the pairing amplitude oscillates as a soliton train described by Jacobi elliptic functions, with robustness against initial fluctuations.

Contribution

It introduces a novel analysis of emergent fermionic pairing dynamics, showing how nonlinear interactions lead to stable soliton train solutions in a time-dependent BCS framework.

Findings

Pairing amplitude oscillates as a Jacobi elliptic function dn.

Soliton train parameters fluctuate but the elliptic form remains robust.

Initial state fluctuations influence parameter variations.

Abstract

We consider evolution of a Fermi gas in the presence of a time-dependent BCS interaction. The pairing amplitude in the emergent BCS state is found to be an oscillatory function of time with predictable characteristics. The interplay of linear instability of the unpaired state and nonlinear interactions selects periodic soliton trains of a specific form, described by the Jacobi elliptic function dn. While the parameters of the soliton train, such as the period, amplitude, and time lag, fluctuate among different realizations, the elliptic function form remains robust. The parameter variation is accounted for by the fluctuations of particle distribution in the initial unpaired state.