Absolutely continuous spectrum of Dirac operators with square-integrable potentials

作者：Hughes Daniel^*; Schmidt Karl Michael

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2014, 144(3): 533-555.

DOI：10.1017/S0308210512001187

We show that the absolutely continuous part of the spectral function of the one-dimensional Dirac operator on a half-line with a constant mass term and a real, square-integrable potential is strictly increasing throughout the essential spectrum (-infinity, -1] boolean OR [1, infinity). The proof is based on estimates for the transmission coefficient for the full-line scattering problem with a truncated potential and a subsequent limiting procedure for the spectral function. Furthermore, we show that the absolutely continuous spectrum persists when an angular momentum term is added, thus also establishing the result for spherically symmetric Dirac operators in higher dimensions.

• 出版日期2014-6