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具有矩形形状的相对论量子台球中的半泊松统计

Semi-Poisson Statistics in Relativistic Quantum Billiards with Shapes of Rectangles.

作者信息

Dietz Barbara

机构信息

Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, Republic of Korea.

出版信息

Entropy (Basel). 2023 May 6;25(5):762. doi: 10.3390/e25050762.

DOI:10.3390/e25050762
PMID:37238517
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC10217041/
Abstract

Rectangular billiards have two mirror symmetries with respect to perpendicular axes and a twofold (fourfold) rotational symmetry for differing (equal) side lengths. The eigenstates of rectangular neutrino billiards (NBs), which consist of a spin-1/2 particle confined through boundary conditions to a planar domain, can be classified according to their transformation properties under rotation by π (π/2) but not under reflection at mirror-symmetry axes. We analyze the properties of these symmetry-projected eigenstates and of the corresponding symmetry-reduced NBs which are obtained by cutting them along their diagonal, yielding right-triangle NBs. Independently of the ratio of their side lengths, the spectral properties of the symmetry-projected eigenstates of the rectangular NBs follow semi-Poisson statistics, whereas those of the complete eigenvalue sequence exhibit Poissonian statistics. Thus, in distinction to their nonrelativistic counterpart, they behave like typical quantum systems with an integrable classical limit whose eigenstates are non-degenerate and have alternating symmetry properties with increasing state number. In addition, we found out that for right triangles which exhibit semi-Poisson statistics in the nonrelativistic limit, the spectral properties of the corresponding ultrarelativistic NB follow quarter-Poisson statistics. Furthermore, we analyzed wave-function properties and discovered for the right-triangle NBs the same scarred wave functions as for the nonrelativistic ones.

摘要

矩形台球对于垂直轴具有两种镜像对称性，并且根据边长不同（相等）具有二重（四重）旋转对称性。矩形中微子台球（NBs）由通过边界条件限制在平面区域内的自旋 - 1/2 粒子组成，其本征态可根据它们在绕π（π/2）旋转下的变换性质进行分类，但不能根据在镜像对称轴上的反射进行分类。我们分析了这些对称性投影本征态以及通过沿其对角线切割得到的相应对称性约化的 NB（即直角三角形 NB）的性质。与它们的边长比例无关，矩形 NB 的对称性投影本征态的谱性质遵循半泊松统计，而完整本征值序列的谱性质表现出泊松统计。因此，与它们的非相对论对应物不同，它们表现得像具有可积经典极限的典型量子系统，其本征态是非简并的，并且随着态数增加具有交替的对称性质。此外，我们发现对于在非相对论极限下表现出半泊松统计的直角三角形，相应的超相对论 NB 的谱性质遵循四分之一泊松统计。此外，我们分析了波函数性质，并发现直角三角形 NB 与非相对论的 NB 具有相同的疤痕波函数。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5545/10217041/d346260fb9eb/entropy-25-00762-g011.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5545/10217041/96401fb3b31f/entropy-25-00762-g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5545/10217041/362473953ee3/entropy-25-00762-g008.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5545/10217041/bed14c4db067/entropy-25-00762-g009.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/5545/10217041/d346260fb9eb/entropy-25-00762-g011.jpg

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本文引用的文献

1
Semiclassical quantization of neutrino billiards.中微子台球的半经典量子化
Phys Rev E. 2020 Oct;102(4-1):042214. doi: 10.1103/PhysRevE.102.042214.
2
Kac's isospectrality question revisited in neutrino billiards.中微子台球中对卡茨等谱性问题的再探讨。
Phys Rev E. 2020 Mar;101(3-1):032215. doi: 10.1103/PhysRevE.101.032215.
3
Ultraslow diffusion and weak ergodicity breaking in right triangular billiards.直角三角形台球中的超慢扩散与弱遍历性破缺
Phys Rev E. 2017 Mar;95(3-1):032209. doi: 10.1103/PhysRevE.95.032209. Epub 2017 Mar 10.
4
Spectral Properties of Dirac Billiards at the van Hove Singularities.狄拉克 billiards 在范霍夫奇点处的谱性质。
Phys Rev Lett. 2016 Jan 15;116(2):023901. doi: 10.1103/PhysRevLett.116.023901. Epub 2016 Jan 14.
5
Nonergodicity and localization of invariant measure for two colliding masses.两个碰撞质量的不变测度的非遍历性与局域化
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Apr;89(4):042918. doi: 10.1103/PhysRevE.89.042918. Epub 2014 Apr 28.
6
Artificial honeycomb lattices for electrons, atoms and photons.人工蜂窝状晶格用于电子、原子和光子。
Nat Nanotechnol. 2013 Sep;8(9):625-33. doi: 10.1038/nnano.2013.161.
7
Distribution of the ratio of consecutive level spacings in random matrix ensembles.随机矩阵系综中连续能隙比的分布。
Phys Rev Lett. 2013 Feb 22;110(8):084101. doi: 10.1103/PhysRevLett.110.084101. Epub 2013 Feb 21.
8
Spin states in graphene quantum dots.石墨烯量子点中的自旋态。
Phys Rev Lett. 2010 Sep 10;105(11):116801. doi: 10.1103/PhysRevLett.105.116801. Epub 2010 Sep 7.
9
Electron-hole crossover in graphene quantum dots.石墨烯量子点中的电子-空穴交叉
Phys Rev Lett. 2009 Jul 24;103(4):046810. doi: 10.1103/PhysRevLett.103.046810.
10
Symmetry classes in graphene quantum dots: universal spectral statistics, weak localization, and conductance fluctuations.石墨烯量子点中的对称类：通用光谱统计、弱局域化和电导涨落。
Phys Rev Lett. 2009 Feb 6;102(5):056806. doi: 10.1103/PhysRevLett.102.056806.