Gross-Pitaevskii vortex motion with critically scaled inhomogeneities

Matthias Kurzke; Jeremy L. Marzuola; Daniel Spirn

doi:10.1137/15M1049014

Gross-Pitaevskii vortex motion with critically scaled inhomogeneities

Matthias Kurzke, Jeremy L. Marzuola, Daniel Spirn

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation i∂_tu = Δu + 1/ϵ² (ρ² ϵ (x) - |u|²). For a unique scaling regime |ρϵ(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.

Original language	English (US)
Pages (from-to)	471-500
Number of pages	30
Journal	SIAM Journal on Mathematical Analysis
Volume	49
Issue number	1
DOIs	https://doi.org/10.1137/15M1049014
State	Published - 2017

Bibliographical note

Publisher Copyright:
© 2017 Society for Industrial and Applied Mathematics.

Keywords

Critical scaling
Gross-Pitaevskii
Vortices

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http://eprints.nottingham.ac.uk/40895/1/M104901.pdf

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abstract = "We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation i∂tu = Δu + 1/ϵ2 (ρ2 ϵ (x) - |u|2). For a unique scaling regime |ρϵ(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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AU - Kurzke, Matthias

AU - Marzuola, Jeremy L.

AU - Spirn, Daniel

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Y1 - 2017

N2 - We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation i∂tu = Δu + 1/ϵ2 (ρ2 ϵ (x) - |u|2). For a unique scaling regime |ρϵ(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.

AB - We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation i∂tu = Δu + 1/ϵ2 (ρ2 ϵ (x) - |u|2). For a unique scaling regime |ρϵ(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.

KW - Critical scaling

KW - Gross-Pitaevskii

KW - Vortices

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EP - 500

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 1

ER -

Gross-Pitaevskii vortex motion with critically scaled inhomogeneities

Abstract

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Keywords

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