The Landscape Law for Tight Binding Hamiltonians

Douglas Arnold; Marcel Filoche; Svitlana Mayboroda; Wei Wang; Shiwen Zhang

doi:10.1007/s00220-022-04494-8

The Landscape Law for Tight Binding Hamiltonians

Douglas Arnold, Marcel Filoche, Svitlana Mayboroda, Wei Wang, Shiwen Zhang

School of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1339-1391
Number of pages	53
Journal	Communications in Mathematical Physics
Volume	396
Issue number	3
DOIs	https://doi.org/10.1007/s00220-022-04494-8
State	Published - Dec 2022

Bibliographical note

Funding Information:
Arnold is supported by the NSF grant DMS-1719694 and Simons Foundation grant 601937, DNA. Filoche is supported by Simons Foundation grant 601944, MF. Mayboroda is supported by NSF DMS 1839077 and the Simons Collaborations in MPS 563916, SM. Wang is supported by Simons Foundation grant 601937, DNA. Zhang is supported in part by the NSF grants DMS1344235, DMS-1839077, and Simons Foundation grant 563916, SM.

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

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title = "The Landscape Law for Tight Binding Hamiltonians",

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author = "Douglas Arnold and Marcel Filoche and Svitlana Mayboroda and Wei Wang and Shiwen Zhang",

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The Landscape Law for Tight Binding Hamiltonians

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