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On the spectrum of the periodic Dirac operator | | L.I. Danilov
; | | Date: |
28 May 2009 | | Abstract: | The absolute continuity of the spectrum for the periodic Dirac operator $$
hat D=sum_{j=1}^n(-ifrac {partial}{partial x_j}-A_j)hat alpha_j + hat
V^{(0)}+hat V^{(1)}, xin R^n, ngeq 3, $$ is proved given that either $Ain
C(R^n;R^n)cap H^q_{loc}(R^n;R^n)$, 2q > n-2, or the Fourier series of the
vector potential $A:R^n o R^n$ is absolutely convergent. Here, $hat
V^{(s)}=(hat V^{(s)})^*$ are continuous matrix functions and $hat V^{(s)}hat
alpha_j=(-1}^shat alpha_jhat V^{(s)}$ for all anticommuting Hermitian
matrices $hat alpha_j$, $hat alpha_j^2=hat I$, s=0,1. | | Source: | arXiv, 0905.4622 | | Services: | Forum | Review | PDF | Favorites | |
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