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Instanton theory and fluctuation corrections to the thermal nucleation rate of a ferromagnetic superfluid

We provide a field-theoretical description of thermal nucleation in a one-dimensional ferromagnetic superfluid, a quantum-gas analogue of false-vacuum decay. The rate at which ground-state domains nucleate follows an Arrhenius law, with an exponential factor determined by a saddle-point of the energy functional -- the critical droplet or instanton -- and a magnitude fixed by small fluctuations about this configuration. We evaluate both contributions over the full parameter space, using a Gel'fand-Yaglom approach to reduce the calculation of the fluctuation spectrum to an initial-value problem. In addition, we obtain a closed-form expression for critical droplets close to the coexistence line, and use it to formulate an effective theory of domain nucleation and growth as a Kramers escape problem for the droplet size. Our results determine the parametric dependence of the nucleation rate and predict its signature in experimental images of a nucleating gas, increasing the rigor of comparisons between nucleation theory and experiment.