Gross--Pitaevskii Vortex Motion with Critically Scaled Inhomogeneities
Gross--Pitaevskii Vortex Motion with Critically Scaled Inhomogeneities
We study the dynamics of vortices in an inhomogeneous Gross--Pitaevskii equation $i \partial_t u = \Delta u + {1\over \varepsilon^2} (\rho_\varepsilon^2(x) - |u|^2)$. For a unique scaling regime $|\rho_\varepsilon(x) - 1 | = O(\log\varepsilon^{-1})$, it is shown that vortices can interact both with the background perturbation and with each other. …