Treffer: Localization for Lipschitz Monotone Quasi-periodic Schrödinger Operators on $$\mathbb Z^d$$ via Rellich Functions Analysis: Localization for Lipschitz monotone quasi-periodic Schrödinger operators on \(\mathbb{Z}^d\) via Rellich functions analysis
Title:
Localization for Lipschitz Monotone Quasi-periodic Schrödinger Operators on $$\mathbb Z^d$$ via Rellich Functions Analysis: Localization for Lipschitz monotone quasi-periodic Schrödinger operators on \(\mathbb{Z}^d\) via Rellich functions analysis
Authors:
Source:
Communications in Mathematical Physics. 406
Publication Status:
Preprint
Publisher Information:
Springer Science and Business Media LLC, 2025.
Publication Year:
2025
Subject Terms:
Mathematics - Spectral Theory, Difference equations, Mathematics - Analysis of PDEs, General mathematical topics and methods in quantum theory, FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Spectral Theory (math.SP), Special classes of linear operators, Mathematical Physics, Analysis of PDEs (math.AP)
Document Type:
Fachzeitschrift
Article
File Description:
application/xml
Language:
English
ISSN:
1432-0916
0010-3616
0010-3616
DOI:
10.1007/s00220-025-05288-4
DOI:
10.48550/arxiv.2407.01970
Access URL:
Rights:
Springer Nature TDM
CC 0
CC 0
Accession Number:
edsair.doi.dedup.....bcc4a581cfe252a58c7b7e262dca617b
Database:
OpenAIRE
Weitere Informationen
We establish the Anderson localization and exponential dynamical localization for a class of quasi-periodic Schrödinger operators on $\mathbb{Z}^d$ with bounded or unbounded Lipschitz monotone potentials via multi-scale analysis based on Rellich function analysis in the perturbative regime. We show that at each scale, the resonant Rellich function uniformly inherits the Lipschitz monotonicity property of the potential via a novel Schur complement argument.
A revised version; to appear in CMP