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Izv. IMI UdGU, 2006, Issue 1(35), Pages 49–76 (Mi iimi79)  

This article is cited in 2 scientific papers (total in 2 papers)

On absolute continuity of the spectrum of three-dimensional periodic Dirac operator

L. I. Danilov

Physical-Technical Institute of the Ural Branch of the Russian Academy of Sciences

Abstract: We prove the absolute continuity of the spectrum of periodic Dirac operator $\sum\limits_{j=1}^3\hat \alpha _j( -i  \frac {\partial}{\partial x_j}-A_j) +\hat {\mathcal V}^{(0)}+\hat {\mathcal V}^{(1)}  , x\in {\mathbb{R}}^3$, with period lattice $\Lambda \subset {\mathbb{R}}^3$ if $A\in L^{\infty}({\mathbb{R}}^3; {\mathbb{R}}^3)$, $\|   |A|  \| _{L^{\infty}({\mathbb{R}}^3)}<\max\limits_{\gamma \in \Lambda \backslash \{ 0\} }\pi |\gamma |^{-1}$, the Hermitian matrix-valued functions $\hat {\mathcal V}^{(s)}_ $ belong to Zigmund class $L^3\ln ^{2+\delta}_ L(K)$ for some $\delta >0$, where $K$ is the unit cell of the lattice $\Lambda$, and $\hat {\mathcal V}^{(s)}\hat \alpha _j=(-1)^s\hat \alpha _j\hat {\mathcal V}^{(s)}$, $s=0,1$, for all anticommuting Hermitian matrices $\hat \alpha _j^   $, $\hat \alpha _j^2=\hat I$, j=1, 2, 3.

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Citation: L. I. Danilov, “On absolute continuity of the spectrum of three-dimensional periodic Dirac operator”, Izv. IMI UdGU, 2006, no. 1(35), 49–76

Citation in format AMSBIB
\Bibitem{Dan06}
\by L.~I.~Danilov
\paper On absolute continuity of the spectrum of three-dimensional periodic Dirac operator
\jour Izv. IMI UdGU
\yr 2006
\issue 1(35)
\pages 49--76
\mathnet{http://mi.mathnet.ru/iimi79}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. I. Danilov, “Absolyutnaya nepreryvnost spektra mnogomernogo periodicheskogo magnitnogo operatora Diraka”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2008, no. 1, 61–96  mathnet
    2. L. I. Danilov, “O spektre periodicheskogo magnitnogo operatora Diraka”, Izv. IMI UdGU, 2016, no. 2(48), 3–21  mathnet  elib
  • Известия Института математики и информатики Удмуртского государственного университета
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