Structure of superscars in a pseudointegrable right-triangular billiard.

IF 2.4 3区 物理与天体物理 Q1 Mathematics
Zhen-Qi Chen, Rui-Hua Ni, Yalei Song, Hong-Ya Xu, Liang Huang
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引用次数: 0

Abstract

Superscars are quantum eigenstates that are localized in an extended region of a family of parallel periodic orbits. They are prevalent in pseudointegrable systems. Here we consider a pseudo-integrable right-triangular quantum billiard with an acute angle π/5 as an example. In the configuration space, we identify and explain a fringe structure of superscar eigenstates originating from a correlation between the two quantum numbers imposed by the sign change rule of the wave function during unfolding. In the wave-vector space, we unveil unique characteristics of the peaks for superscar states, and in return, exploit these features to determine the family of periodic orbits and the corresponding quantum numbers without ambiguity. We also find that the eigenstates can be superpositions not only of superscar modes corresponding to different families of periodic orbits, but also of superscar modes corresponding to the same family but with different sets of quantum numbers, which poses a challenge for conventional approaches in identifying the superscar modes but can be addressed properly by our analysis. These results are also applicable to superscar states in other pseudointegrable systems.

伪可积直角三角形台球中超痕的结构。
超伤疤是一种量子本征态,定位于一组平行周期轨道的扩展区域。它们普遍存在于伪可积系统中。本文以锐角为π/5的伪可积直角三角形量子台球为例。在组态空间中,我们识别并解释了由波函数的符号变化规则在展开过程中施加的两个量子数之间的相关性产生的超疤痕特征态的条纹结构。在波向量空间中,我们揭示了超疤痕态峰的独特特征,并反过来利用这些特征来确定周期轨道族和相应的量子数。我们还发现本征态不仅可以是不同周期轨道族对应的超疤痕模的叠加,也可以是同一族对应的不同量子数集的超疤痕模的叠加,这对传统方法识别超疤痕模提出了挑战,但我们的分析可以很好地解决这个问题。这些结果同样适用于其他伪可积系统的超疤痕态。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Physical review. E
Physical review. E 物理-物理:流体与等离子体
CiteScore
4.60
自引率
16.70%
发文量
0
审稿时长
3.3 months
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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