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Title: Electronic structure of defects in the Thomas-Fermi-von-Weizsäcker model of crystals
Author: Nazar, Faizan Q.
ISNI:       0000 0004 6423 7859
Awarding Body: University of Warwick
Current Institution: University of Warwick
Date of Award: 2017
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In this thesis, we establish a locality property for solutions to the Thomas-Fermi-von Weizsäcker (TFW) equations. This is a system of coupled PDEs that models the ground state electron density corresponding to a given nuclear arrangement. The locality property is a pointwise stability estimate for the TFW equations, that demonstrates the exponential response of the electron density to a perturbation of the nuclei. We show that this result holds for the TFW when using either the Coulomb or the Yukawa potential to treat the interaction of charged particles. We then use the locality result to prove several consequences for the TFW ground state, which includes generalising results from [14] regarding the neutrality of infinite systems and also showing the uniform convergence of ground states when passing to the limit from the Yukawa to the Coulomb model. Our main application is the construction of site energies from the TFW energy. The locality result implies that the response of each site energy decays exponentially with respect to a perturbation of the nuclear arrangement. Using these site energies, we then formulate the lattice relaxation problem, that was initially formulated in [23], to consider the response of a perfect crystal lattice to the introduction of a point defect. The site energies allow us to formulate a variational problem over a space of deformations of the lattice, show this problem is well-posed and finally establish the decay properties of minimisers.
Supervisor: Not available Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics