= Thermodynamic vortex-nucleation frequency
{title2=$\Omega_c=\Delta E/\Delta L_z$}
A <quantum vortex> becomes energetically favourable in a <rotating reference frame> when $\Delta E-\Omega\Delta L_z<0$. For a singly <quantized vortex> in a long radially Thomas–Fermi condensate, the cutoff-shell estimate is
$$
\Omega_c\simeq\frac{2\hbar}{mR_r^2}\left[\log\frac{R_r}{a_0}-\frac12\right].
$$
Integrating the trapped <number density> against $u_\theta^2$ produces the <logarithm> and constant; integrating it against <angular momentum> per particle gives $\Delta L_z\simeq\pi Hn_0\hbar R_r^2/2$. Resolved-core corrections can alter the nonlogarithmic constant. This criterion compares equilibrium rotating-frame energies and does not remove a dynamical vortex-entry barrier.
Back to article page
