Abstract
We consider the development of pairing in an ideal Fermi gas in the presence of a time-dependent BCS interaction. The pairing amplitude time evolution is controlled by the interplay of linear instability of the unpaired state and nonlinear interactions which limit the growth. This results in oscillatory time dependence with predictable characteristics, selecting periodic soliton trains of a specific form, described by a Jacobi elliptic function. 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 fluctuations are accounted for by the randomness of particle distribution in the initial unpaired state.
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