论文标题
量子几何限制和Grushin圆柱体中的动态传输
Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder
论文作者
论文摘要
我们对在配备有不完整的Grushin类型的无限型圆柱体上定义的Laplace-Beltrami操作员的自我参与实现，该指标产生了无限缺陷指数。这种实现自然被解释为统治schrödinger量子粒子远离奇异性或跨越奇异性的动态传播的哈密顿人。特别是，我们表征了所有具有明确的局部边界条件在奇异性下的物理有意义的扩展。在我们的一般分类中，我们检索了那些先前在最近的文献中鉴定出的杰出扩展，即最狭窄和传播最多的扩展。
We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder equipped with an incomplete Riemannian metric of Grushin type, in the class of metrics yielding an infinite deficiency index. Such realisations are naturally interpreted as Hamiltonians governing the geometric confinement of a Schrödinger quantum particle away from the singularity, or the dynamical transmission across the singularity. In particular, we characterise all physically meaningful extensions qualified by explicit local boundary conditions at the singularity. Within our general classification we retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting one.
