三维软量子波导
Soft quantum waveguides in three dimensions
摘要：
本文讨论了三维软量子波导，即$\R^3$中的薛定谔算符，其吸引势由无限长管支撑，并保持其横截面不变。我们表明，如果管是渐近直的，它的两端之间的距离是无界的，它的扭曲满足所谓的唐条件，本质谱是不受光滑弯曲。此外，我们得到了一个充分条件，表示在管的几何形状，这样的运营商的离散谱是非空的。
英文摘要：
We discuss a three-dimensional soft quantum waveguide, in other words, Schrödinger operator in $\R^3$ with an attractive potential supported by an infinite tube and keeping its transverse profile fixed. We show that if the tube is asymptotically straight, the distance between its ends is unbounded, and its twist satisfies the so-called Tang condition, the esential spectrum is not affected by smooth bends. Furthermore, we derive a sufficient condition, expressed in terms of the tube geometry, for the discrete spectrum of such an operator to be nonempty.
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