학술논문
The Landscape Law for Tight Binding Hamiltonians.
Document Type
Article
Source
Subject
*SCHRODINGER operator
*DENSITY of states
*
Language
ISSN
0010-3616
Abstract
The present paper extends the landscape theory pioneered in Filoche and Mayboroda (Proc Natl Acad Sci USA 109(37):14761–14766, 2012), Arnold et al. (Commun Partial Differ Equ 44(11):1186–1216, 2019) and David et al. (Adv Math 390:107946, 2021) to the tight-binding Schrödinger operator on Z d . In particular, we establish upper and lower bounds for the integrated density of states in terms of the counting function based upon the localization landscape. [ABSTRACT FROM AUTHOR]