论文标题
与关键壳相互作用的曲率对狄拉克运算符的基本范围的贡献
Curvature contribution to the essential spectrum of Dirac operators with critical shell interactions
论文作者
论文摘要
我们讨论了三维狄拉克运算符的光谱特性，其静电和洛伦兹标量壳相互作用的关键组合由紧凑的光滑表面支撑。事实证明，相互作用的关键性可能会导致基本频谱的新间隔。间隔的位置和长度由耦合常数和表面的主要曲率明确控制。与迄今为止考虑的较低维临界情况或特殊几何形状相比，这种效果是全新的，在此，在基本频谱中只有一个新点。
We discuss the spectral properties of three-dimensional Dirac operators with critical combinations of electrostatic and Lorentz scalar shell interactions supported by a compact smooth surface. It turns out that the criticality of the interaction may result in a new interval of essential spectrum. The position and the length of the interval are explicitly controlled by the coupling constants and the principal curvatures of the surface. This effect is completely new compared to lower dimensional critical situations or special geometries considered up to now, in which only a single new point in the essential spectrum was observed.
