The discrete magnetic Laplacian: geometric and spectral preorders with applications

Mención Internacional en el título de doctor In the present dissertation, we are interested in the spectral properties of the magnetic Laplacian. We study the spectrum of the Magnetic Laplacian under some geometrical perturbation on the graph. In particular, we are interested in the existence of spe...

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Bibliographic Details
Published in:Linear Algebra and its Applications
Main Author: Fabila Carrasco, John Stewart
Other Authors: Lledó Macau, Fernando, UC3M. Departamento de Matemáticas, Ministerio de Economía y Competitividad (España)
Format: Doctoral or Postdoctoral Thesis
Language:English
Published: 2020
Subjects:
Magnetic
Spectrum
Graph theory
Discrete Laplacian
Magnetic Laplacian
Matemáticas
DML
Online Access:http://hdl.handle.net/10016/31372
Description
Summary:Mención Internacional en el título de doctor In the present dissertation, we are interested in the spectral properties of the magnetic Laplacian. We study the spectrum of the Magnetic Laplacian under some geometrical perturbation on the graph. In particular, we are interested in the existence of spectral gaps, i.e., intervals that do not contain spectrum. We begin this dissertation giving a general context and a brief summary of some studies about the DML and in relation to the work in this thesis. Este trabajo fue apoyado por el Ministerio de Economía y Competitividad mediante los programas DGI MTM2014-54692-P y MTM2017-84098-P. Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de Madrid Presidente: Carlos Marijuán López.- Secretario: Julio Íñigo de Vicente Majua.- Vocal: Natalia Saburova

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