On the Lipschitz continuity of spectral bands of Harper-like and magnetic Schrödinger operators

Horia Cornean

doi:10.1007/s00023-010-0048-1

On the Lipschitz continuity of spectral bands of Harper-like and magnetic Schrödinger operators

Horia Cornean

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

15 Citations (Scopus)

Abstract

We show for a large class of discrete Harper-like and continuous magnetic Schrödinger operators that their band edges are Lipschitz continuous with respect to the intensity of the external constant magnetic field. We generalize a result obtained by Bellissard (Commun Math Phys 160:599–613, 1994), and give examples in favor of a recent conjecture of G. Nenciu.

Original language	English
Journal	Annales Henri Poincare
Volume	11
Issue number	5
Pages (from-to)	973-990
Number of pages	18
ISSN	1424-0637
DOIs	https://doi.org/10.1007/s00023-010-0048-1
Publication status	Published - 2010

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title = "On the Lipschitz continuity of spectral bands of Harper-like and magnetic Schr{\"o}dinger operators",

abstract = "We show for a large class of discrete Harper-like and continuous magnetic Schr{\"o}dinger operators that their band edges are Lipschitz continuous with respect to the intensity of the external constant magnetic field. We generalize a result obtained by Bellissard (Commun Math Phys 160:599–613, 1994), and give examples in favor of a recent conjecture of G. Nenciu. ",

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T1 - On the Lipschitz continuity of spectral bands of Harper-like and magnetic Schrödinger operators

AU - Cornean, Horia

PY - 2010

Y1 - 2010

N2 - We show for a large class of discrete Harper-like and continuous magnetic Schrödinger operators that their band edges are Lipschitz continuous with respect to the intensity of the external constant magnetic field. We generalize a result obtained by Bellissard (Commun Math Phys 160:599–613, 1994), and give examples in favor of a recent conjecture of G. Nenciu.

AB - We show for a large class of discrete Harper-like and continuous magnetic Schrödinger operators that their band edges are Lipschitz continuous with respect to the intensity of the external constant magnetic field. We generalize a result obtained by Bellissard (Commun Math Phys 160:599–613, 1994), and give examples in favor of a recent conjecture of G. Nenciu.

U2 - 10.1007/s00023-010-0048-1

DO - 10.1007/s00023-010-0048-1

M3 - Journal article

SN - 1424-0637

VL - 11

SP - 973

EP - 990

JO - Annales Henri Poincare

JF - Annales Henri Poincare

IS - 5

ER -

On the Lipschitz continuity of spectral bands of Harper-like and magnetic Schrödinger operators

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