https://github.com/cshaa/thesis-magnetic-transport

A bachelor's thesis on Quantum Mechanics
https://github.com/cshaa/thesis-magnetic-transport

latex quantum-mechanics thesis

Last synced: 17 days ago
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A bachelor's thesis on Quantum Mechanics

• Host: GitHub
• URL: https://github.com/cshaa/thesis-magnetic-transport
• Owner: cshaa
• Created: 2021-01-30T12:31:50.000Z (about 4 years ago)
• Default Branch: main
• Last Pushed: 2023-09-05T13:25:09.000Z (over 1 year ago)
• Last Synced: 2025-01-17T21:12:59.193Z (25 days ago)
• Topics: latex, quantum-mechanics, thesis
• Language: Mathematica
• Homepage:
• Size: 33.9 MB
• Stars: 2
• Watchers: 3
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# Magnetic Transport Along Translationally Invariant Obstacles

A thesis by Michal Grňo, supervised by prof. Pavel Exner.

## Links

 * [The thesis in PDF](https://github.com/m93a/thesis-magnetic-transport/blob/main/thesis/thesis.pdf)

 * [Supervisor's review](https://github.com/m93a/thesis-magnetic-transport/blob/main/review_supervisor.pdf) (in Czech)

 * [Opponent's review](https://github.com/m93a/thesis-magnetic-transport/blob/main/review_opponent.pdf)

## Abstract

We discuss the spectra of magnetic Schrödinger operators of the form ${(-\mathrm i\nabla + \vec{A}(x))^2 + V(x)}$ on ${L^2(\Omega)}$, where $\Omega$ is either $\mathbb R^2$, a half-plane, a strip, or a thin layer in $\mathbb R^3$. This class of operators includes the Landau Hamiltonian, as well as the Iwatsuka Hamiltonian and other translationally invariant perturbations of it. We provide a comprehensive list of the known results regarding these operators, and inspect two Hamiltonians that have not yet been studied: the Landau Hamiltonian with a $\delta$-interaction supported on a line and the Landau Hamiltonian in a half-plane with a Robin boundary condition. We prove that the spectra of these two Hamiltonians are purely absolute continuous and that the former has gaps between adjacent Landau levels.

## Template

The template used for the TeX document was made by:

 * Martin Mareš  – správce šablony

 * Arnošt Komárek 

 * Michal Kulich