The Dry Ten Martini Problem for Sturmian Hamiltonians

Ram Band, Siegfried Beckus, Raphael Loewy

Type: Preprint

Publication Date: 2024-02-26

Citations: 0

DOI: https://doi.org/10.48550/arxiv.2402.16703

Abstract

The Dry Ten Martini Problem for Sturmian Hamiltonians is affirmatively solved. Concretely, we prove that all spectral gaps are open for Schr\"odinger operators with Sturmian potentials and non-vanishing coupling constant. A key approach towards the solution is a representation of the spectrum as the boundary of an infinite tree. This tree is constructed via particular periodic approximations and it encodes substantial spectral characteristics.

Locations

arXiv (Cornell University) - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	A note on discrete Borg-type theorems	2017	V. B. Kiran Kumar G. Krishna Kumar
+ PDF Chat	A review of a work by Raymond: Sturmian Hamiltonians with a large coupling constant -- periodic approximations and gap labels	2024	Ram Band Siegfried Beckus Barak Biber L. Raymond Y. Thomas
+	Dry Ten Martini Problem in the non-critical case	2023	Artur Avila Jiangong You Qi Zhou
+	Gaps in the Spectrum of the Maxwell Operator with Periodic Coefficients	2003	N. Filonov
+	Gap Labelling Theorems for Schrödinger Operators	1992	Jean Bellissard
+ PDF Chat	Spectral Gaps for Periodic Schr�dinger Operators with Strong Magnetic Fields	2004	Yuri A. Kordyukov
+ PDF Chat	Non-periodic One-gap Potentials in Quantum Mechanics	2018	Dmitry Zakharov В. Е. Захаров
+	The Spectrum of the Almost Mathieu Operator	2009	David Damanik
+	Universal algorithms for computing spectra of periodic operators	2021	Jonathan Ben-Artzi Marco Marletta Frank Rösler
+	A periodic Schrödinger operator with two degenerate spectral gaps (Spectral and Scattering Theory and Related Topics)	2014	Hiroaki Niikuni
+	A Pseudospectral Analogue of Discrete Borg-type Theorems	2016	V. B. Kiran Kumar G. Krishna Kumar
+	The density of states for almost periodic Schr�dinger operators and the frequency module: A counter-example	1982	Jean Bellissard Elisabetta Scoppola
+	On the Inverse Spectral Problem for the Quasi-Periodic Schr\"odinger Equation	2012	David Damanik Michael Goldstein
+	On the Inverse Spectral Problem for the Quasi-Periodic Schrödinger Equation	2012	David Damanik Michael A. Goldstein
+	Polynomial decay of the gap length for C quasi-periodic Schrödinger operators and spectral application	2021	Ao Cai Xueyin Wang
+ PDF Chat	Dispersion for Schrödinger operators on regular trees	2022	Kaïs Ammari Mostafa Sabri
+ PDF Chat	Dirac operators with periodic δ-interactions: Spectral gaps and inhomogeneous Diophantine approximation	2009	Kazushi Yoshitomi
+	A periodic schrödinger operator with two degenerate spectral gaps	2012	Hiroaki Niikuni
+ PDF Chat	Must the Spectrum of a Random Schr\"odinger Operator Contain an Interval?	2021	David Damanik Anton Gorodetski
+	Structure of the spectrum of infinite dimensional Hamiltonian operators	2008	Alatancang Junjie Huang Fan Xiao-Ying

Works That Cite This (0)

Action	Title	Year	Authors

Works Cited by This (0)

Action	Title	Year	Authors