Vortex dynamics in the Ginzburg-Landau and Maxwell-Klein-Gordon models with pinning

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Wileman, Paul (2021) Vortex dynamics in the Ginzburg-Landau and Maxwell-Klein-Gordon models with pinning. PhD thesis, University of Nottingham.

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Abstract

We study the motion of vortices in a superconductor subject to a perturbed background potential. Such a potential models the presence of pinning sites in the superconductor which the vortices are attracted to. The pinning potential is scaled such that the intervortex interactions also play a role in the vortex dynamics. We use the time-dependent Ginzburg-Landau model to relate the vortex velocities to forces in the system; namely, the gradient of the renormalized energy which accounts for intervortex interactions and the gradient of the pinning potential. We make an effort to include the gauge terms at every step. Additionally, we include both parabolic motion and Schrodinger flow from the outset which results in a mixed-flow dynamical law.

In the second part of the thesis we shift to the Maxwell-Klein-Gordon model with a pinned Ginzburg-Landau potential to model the motion of vortices in a different mathematical framework. The equations are now second-order in time (compared to the first-order in time Ginzburg-Landau equations) so proves that the methods applied in the first part of the thesis are robust and can be adapted to a model with greater complexity. We derive a dynamical law for vortices exposed to the critically scaled pinning potential and experiencing interactions from other vortices in the system.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Kurzke, Matthias
Keywords: vortex motion, vortex dynamics, pinning, superconductor
Subjects: Q Science > QA Mathematics > QA801 Analytic mechanics
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 64438
Depositing User: Wileman, Paul
Date Deposited: 09 Jun 2021 14:05
Last Modified: 09 Jun 2021 14:05
URI: https://eprints.nottingham.ac.uk/id/eprint/64438

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