论文标题
二维狄拉克运算符，一般$δ$ - 壳交互在直线上支持
Two-dimensional Dirac operators with general $δ$-shell interactions supported on a straight line
论文作者
论文摘要
在本文中，将在直线上支持的二维狄拉克运算符带有一个普通的Hermitian $δ$壳相互作用作为自动接合操作员，并详细研究了其光谱属性。特别是，可以证明奇异连续频谱总是空的，并且通过切换某个$δ$ shell的相互作用，可以在自由操作员频谱的间隙中生成特征值，或者部分或部分或完全关闭差距。这表明，所研究的运营商可以用作有趣的连续玩具模型。最后，提出了具有常规电势的狄拉克操作员的近似值。
In this paper the two-dimensional Dirac operator with a general hermitian $δ$-shell interaction supported on a straight line is introduced as a self-adjoint operator and its spectral properties are investigated in detail. In particular, it is demonstrated that the singularly continuous spectrum is always empty and that by switching a certain $δ$-shell interaction on, it is possible to generate an eigenvalue in the gap of the spectrum of the free operator or to partially or even fully close the gap. This suggests that the studied operators may serve as interesting continuum toy-models for Dirac materials. Finally, approximations by Dirac operators with regular potentials are presented.
