Stochastic longevity of a dark soliton in a finite-temperature Bose-Einstein condensate

We study the decay of a dark soliton in a homogeneous Bose-Einstein condensate. We give an analytical treatment of a decaying soliton, deriving an expression for the soliton velocity and decay time in the absence of thermal noise. We test the result against numerical simulations of a spatially confined system and find good agreement in the regime of low temperature ($k_BT\ll \mu$). Thermal fluctuations are found to slow the escape of the soliton, extending its lifetime beyond the predictions of the noise-free theory; the effect becomes significant at a characteristic temperature $k_BT\sim \mu$. This stabilization by noise allows us to infer an analytical lower bound for the dark soliton decay time.