Gross-Pitaevskii vortex motion with critically scaled inhomogeneities

Kurzke, Matthias; Marzuola, Jeremy L.; Spirn, Daniel

Abstract

We study the dynamics of vortices in an inhomogeneous Gross--Pitaevskii equation iδtu = Δu + 1/ε²(ρ² ε(ᵡ) - |u|²). For a unique scaling regime |ρε(ᵡ) - 1 = O(logε¯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.

Citation

Kurzke, M., Marzuola, J. L., & Spirn, D. (2017). Gross-Pitaevskii vortex motion with critically scaled inhomogeneities. SIAM Journal on Mathematical Analysis, 49(1), 471-500. https://doi.org/10.1137/15M1049014

• Journal Article Type: Article
• Acceptance Date: Nov 17, 2016
• Online Publication Date: Feb 16, 2017
• Publication Date: Feb 16, 2017
• Deposit Date: Feb 28, 2017
• Publicly Available Date: Feb 28, 2017
• Journal: SIAM Journal on Mathematical Analysis
• Print ISSN: 0036-1410
• Electronic ISSN: 0036-1410
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 49
• Issue: 1
• Pages: 471-500
• DOI: https://doi.org/10.1137/15M1049014
• Keywords: Vortices, Gross-Pitaevskii, Critical scaling
• Public URL: https://nottingham-repository.worktribe.com/output/845470
• Publisher URL: http://epubs.siam.org/doi/10.1137/15M1049014
• Additional Information: First published in SIAM Journal on Mathematical Analysis in Vol. 49, no. 1, published by the Society for Industrial and Applied Mathematics (SIAM) c2017 Society for Industrial and Applied Mathematics