论文标题
螺旋形量子波导的光谱特性
Spectral properties of spiral-shaped quantum waveguides
论文作者
论文摘要
我们研究了局限于硬壁螺旋形区域的粒子的性质。作为一个案例研究，我们详细分析了阿基米德螺旋形，该螺旋的频谱超过连续阈值绝对远离阈值。但是，径向宽度和垂直宽度之间的细微差异意味着，与“不太弯曲”波导相比，在这种情况下，离散频谱是空的。我们还讨论了具有中央空腔的多臂阿基赛马螺旋和螺旋波导的修改。在后一种情况下，如果腔超过临界大小，则已经存在绑定状态。对于更一般的螺旋区域，光谱性质取决于它们是“扩展”还是“缩小”。最有趣的情况发生在渐近的阿基米德案件中，其中结合状态的存在取决于达到渐近性的方向。
We investigate properties of a particle confined to a hard-wall spiral-shaped region. As a case study we analyze in detail the Archimedean spiral for which the spectrum above the continuum threshold is absolutely continuous away from the thresholds. The subtle difference between the radial and perpendicular width implies, however, that in contrast to `less curved' waveguides, the discrete spectrum is empty in this case. We also discuss modifications such a multi-arm Archimedean spirals and spiral waveguides with a central cavity; in the latter case bound state already exist if the cavity exceeds a critical size. For more general spiral regions the spectral nature depends on whether they are `expanding' or `shrinking'. The most interesting situation occurs in the asymptotically Archimedean case where the existence of bound states depends on the direction from which the asymptotics is reached.
