Dirac方程的特征函数的迹公式

Trace Formulae for the Eigenfunctions of Periodic Finite-Bands Dirac Operator

中文关键词:  迹公式  特征函数  周期N-bands Dirac算子

英文关键词:trace formulae  eigenfunctions  periodic \textit{N}-bands Dirac operator

中文摘要:

      本文研究具有周期有限带位势的Dirac算子, 利用Dirac算子与单值算子的交换性,定义Bloch函数和乘子曲线, 进而获得揭示Bloch函数与位势间内在关系的Dubrovin-Novikov型公式; 通过复球面上的留数计算, 最终分别得到相应于谱带左端点、右端点以及双侧端点的特征函数的迹公式.

英文摘要:

      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.