Gross-Pitaevskii vortex motion with critically-scaled inhomogeneities

2015/10/27 by Kurzke, Matthias, Marzuola, Jeremy L., Spirn, Daniel
#35Q60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1510.08093

Abstract

We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation i ∂_t u = Δu + 1\over ε² (p_ε²(x) - |u|²). For a unique scaling regime |p_ε(x) - 1 | = O(|log ε|^-1), it is shown that vortices can interact both with the background perturbation and with each other. Results for associated parabolic and elliptic problems are discussed.

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