| Trace Formulae for the Eigenfunctions of Periodic Finite-Bands Dirac Operator |
| Received:June 02, 2014 Revised:March 09, 2015 |
| Key Words:
trace formulae eigenfunctions periodic \textit{N}-bands Dirac operator
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11326131), the Natural Science Foundation of Zhejiang Province (Grant No.LQ14A010009) and the Natural Science Foundation of Huzhou City (Grant No.2013YZ06). |
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| Abstract: |
| In this paper, we deal with a Dirac operator with periodic and finite-bands potentials. Taking advantage of the commutativity of the monodromy operator and the Dirac operator, we define the Bloch functions and multiplicator curve. Further, we obtain the formulae of Dubrovin-Novikov's type, which illustrate the inherent relations between the Bloch functions and potentials. Finally, we get the trace formulae of eigenfunctions corresponding to the left end-points, right end-points and all end-points of the spectral bands by calculation of residues on the complex sphere, respectively. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2015.05.002 |
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