标题： 紧致八边形上的分形与疤痕 显示英文标题

标题： Fractals and Scars on a Compact Octagon

摘要： 一个有限的宇宙自然支持混沌的经典运动。在经典动力学中，我们完全描述了一种有序的分形结构，它从一个紧致的二维八边形的混沌动力学中显现出来。在经典到量子的过渡中，底层的分形可能以疤痕的形式持续存在，疤痕是半经典波函数中增强振幅的脊线。尽管八边形上的疤痕较弱，但我们提出了有限宇宙中分形和疤痕可能存在的微妙影响。 显示英文摘要

摘要： A finite universe naturally supports chaotic classical motion. An ordered fractal emerges from the chaotic dynamics which we characterize in full for a compact 2-dimensional octagon. In the classical to quantum transition, the underlying fractal can persist in the form of scars, ridges of enhanced amplitude in the semiclassical wave function. Although the scarring is weak on the octagon, we suggest possible subtle implications of fractals and scars in a finite universe.