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On the spectrum of (non)magnetic Schrödinger operators

Miranda, Germán LU orcid (2025)
Abstract
This thesis investigates the spectral properties of magnetic and nonmagnetic Schrödinger operators, which have
applications in the distribution of superconductivity in type II superconductors and wave theory. The thesis begins
with an introduction to the main results in the field, giving a more detailed presentation for clarity. Next, we focus
on the original research articles conducted by the author in collaboration with others. We provide one of the first
counterexamples in three dimensions to the monotonicity of the lowest eigenvalue of the magnetic Laplacian. The
spectrum of the magnetic Laplacian is further analysed in general domains under a piecewise constant magnetic
field and in the disc under a constant... (More)
This thesis investigates the spectral properties of magnetic and nonmagnetic Schrödinger operators, which have
applications in the distribution of superconductivity in type II superconductors and wave theory. The thesis begins
with an introduction to the main results in the field, giving a more detailed presentation for clarity. Next, we focus
on the original research articles conducted by the author in collaboration with others. We provide one of the first
counterexamples in three dimensions to the monotonicity of the lowest eigenvalue of the magnetic Laplacian. The
spectrum of the magnetic Laplacian is further analysed in general domains under a piecewise constant magnetic
field and in the disc under a constant magnetic field. Lastly, we present a new approach to the comparison of
eigenvalues of the Laplacian under different boundary conditions. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Doc. Rohleder, Jonathan, Stockholm University, Sweden.
organization
publishing date
type
Thesis
publication status
published
subject
publisher
Centre for Mathematical Sciences, Lund University
defense location
Lecture Hall MH:Hörmander, Centre of Mathematical Sciences, Märkesbacken 4, Faculty of Engineering LTH, Lund University, Lund.
defense date
2025-10-24 13:00:00
ISBN
978-91-8104-585-7
978-91-8104-586-4
language
English
LU publication?
yes
id
988744b4-9ca5-4c38-ad53-9683463a1053
date added to LUP
2025-09-09 13:25:38
date last changed
2025-10-02 03:28:09
@phdthesis{988744b4-9ca5-4c38-ad53-9683463a1053,
  abstract     = {{This thesis investigates the spectral properties of magnetic and nonmagnetic Schrödinger operators, which have<br/>applications in the distribution of superconductivity in type II superconductors and wave theory. The thesis begins<br/>with an introduction to the main results in the field, giving a more detailed presentation for clarity. Next, we focus<br/>on the original research articles conducted by the author in collaboration with others. We provide one of the first<br/>counterexamples in three dimensions to the monotonicity of the lowest eigenvalue of the magnetic Laplacian. The<br/>spectrum of the magnetic Laplacian is further analysed in general domains under a piecewise constant magnetic<br/>field and in the disc under a constant magnetic field. Lastly, we present a new approach to the comparison of<br/>eigenvalues of the Laplacian under different boundary conditions.}},
  author       = {{Miranda, Germán}},
  isbn         = {{978-91-8104-585-7}},
  language     = {{eng}},
  publisher    = {{Centre for Mathematical Sciences, Lund University}},
  school       = {{Lund University}},
  title        = {{On the spectrum of (non)magnetic Schrödinger operators}},
  url          = {{https://lup.lub.lu.se/search/files/227308431/e-spik_ex_german.pdf}},
  year         = {{2025}},
}