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Schrödinger Operator on the Zigzag Half-Nanotube in Magnetic Field

Published online by Cambridge University Press:  12 May 2010

A. Iantchenko  and
E. Korotyaev
A. Iantchenko*
Affiliation:
Institute of Mathematics and Physics, Aberystwyth Univ., Penglais, Ceredigion, SY23 3BZ, UK
E. Korotyaev
Affiliation:
School of Mathematics, Cardiff Univ., Senghennydd Road, Cardiff, CF24 4AG, UK
*
* Corresponding author. E-mail: ai@mah.se
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Abstract

We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schrödinger operator with a periodic potential plus a finitely supported perturbation. We describe all eigenvalues and resonances of this operator, and theirs dependence on the magnetic field. The proof is reduced to the analysis of the periodic Jacobi operators on the half-line with finitely supported perturbations.

Keywords

nanotubesJacobi operatorperiodicfinite support perturbationresonances
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 4: Spectral problems. Issue dedicated to the memory of M. Birman , 2010 , pp. 175 - 197
Copyright
© EDP Sciences, 2010

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