Absolutely continuous spectrum for quantum trees

We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling constants and potentials on the edges. We show the spectrum consists of bands of purely absolutely continuous spectrum,...

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Main Authors: Nalini Anantharaman, Maxime Ingremeau, Mostafa Sabri, Brian Winn
Format: Default Article
Published: 2021
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Online Access:https://hdl.handle.net/2134/13084724.v1
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spelling rr-article-130847242021-02-18T00:00:00Z Absolutely continuous spectrum for quantum trees Nalini Anantharaman (9514244) Maxime Ingremeau (7159790) Mostafa Sabri (7159793) Brian Winn (1247334) Foundations of quantum mechanics Mathematical Physics Pure Mathematics trees random operators quantum graphs Absolutely continuous spectrum Quantum Mechanics We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling constants and potentials on the edges. We show the spectrum consists of bands of purely absolutely continuous spectrum, along with a discrete set of eigenvalues. Afterwards, we study random perturbations of such trees, at the level of edge length and coupling, and prove the stability of pure AC spectrum, along with resolvent estimates. 2021-02-18T00:00:00Z Text Journal contribution 2134/13084724.v1 https://figshare.com/articles/journal_contribution/Absolutely_continuous_spectrum_for_quantum_trees/13084724 CC BY 4.0
institution Loughborough University
collection Figshare
topic Foundations of quantum mechanics
Mathematical Physics
Pure Mathematics
trees
random operators
quantum graphs
Absolutely continuous spectrum
Quantum Mechanics
spellingShingle Foundations of quantum mechanics
Mathematical Physics
Pure Mathematics
trees
random operators
quantum graphs
Absolutely continuous spectrum
Quantum Mechanics
Nalini Anantharaman
Maxime Ingremeau
Mostafa Sabri
Brian Winn
Absolutely continuous spectrum for quantum trees
description We study the spectra of quantum trees of finite cone type. These are quantum graphs whose geometry has a certain homogeneity, and which carry a finite set of edge lengths, coupling constants and potentials on the edges. We show the spectrum consists of bands of purely absolutely continuous spectrum, along with a discrete set of eigenvalues. Afterwards, we study random perturbations of such trees, at the level of edge length and coupling, and prove the stability of pure AC spectrum, along with resolvent estimates.
format Default
Article
author Nalini Anantharaman
Maxime Ingremeau
Mostafa Sabri
Brian Winn
author_facet Nalini Anantharaman
Maxime Ingremeau
Mostafa Sabri
Brian Winn
author_sort Nalini Anantharaman (9514244)
title Absolutely continuous spectrum for quantum trees
title_short Absolutely continuous spectrum for quantum trees
title_full Absolutely continuous spectrum for quantum trees
title_fullStr Absolutely continuous spectrum for quantum trees
title_full_unstemmed Absolutely continuous spectrum for quantum trees
title_sort absolutely continuous spectrum for quantum trees
publishDate 2021
url https://hdl.handle.net/2134/13084724.v1
_version_ 1805250671253913600