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

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Title
Semi-Poisson Statistics in Relativistic Quantum Billiards with Shapes of Rectangles
Author(s)
Barbara Dietz
Publication Date
2023-05
Journal
Entropy, v.25, no.5
Publisher
MDPI
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 (Formula presented.) ((Formula presented.)) 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. © 2023 by the author.
URI
https://pr.ibs.re.kr/handle/8788114/13498
DOI
10.3390/e25050762
ISSN
1099-4300
Appears in Collections:
Center for Theoretical Physics of Complex Systems(복잡계 이론물리 연구단) > 1. Journal Papers (저널논문)
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