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On Absolute Continuity of the Spectrum of a 3D Periodic Magnetic Dirac Operator

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Abstract

Absolute continuity of the spectrum of a 3D periodic magnetic Dirac operator is proved provided that the magnetic potential A belongs to the space \({H^q_{\mathrm{loc}},q >1 }\) , and the matrix potential \({\widehat V\in L^3_{\mathrm {loc}}}\) is represented in the form \({\widehat V=\widehat V_0+\widehat V_1}\) , where \({\widehat V_0}\) commutes and \({\widehat V_1}\) anticommutes with the Dirac matrices \({\widehat \alpha _j, j = 1, 2, 3}\) .

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  1. Physical-Technical Institute, Kirov street, 132, 420000, Izhevsk, Russia

    Leonid I. Danilov

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  1. Leonid I. Danilov
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Danilov, L.I. On Absolute Continuity of the Spectrum of a 3D Periodic Magnetic Dirac Operator. Integr. Equ. Oper. Theory 71, 535–556 (2011). https://doi.org/10.1007/s00020-011-1906-z

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  • DOI: https://doi.org/10.1007/s00020-011-1906-z

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