Loss-driven onset of condensate stirring
= Loss-driven onset of condensate stirring
{title2=$R(t)=R(0)e^{-t/(4\tau)}$}
For a <two-dimensional Thomas–Fermi condensate> at fixed coupling, $N=\pi n_0R^2/2\propto\mu^2$, so $R\propto N^{1/4}$. Slow exponential atom loss shrinks the cloud while a fixed stirring radius becomes a larger fraction of its size. At $\Omega=\omega_r/\sqrt2$ and initial $D/R=1/2$, the local-sound-speed threshold is reached at $t_c=2\tau\ln2$, before the shrinking cloud edge reaches the beam.