Eigenphase distributions of unimodular circular ensembles

IF 3.5 4区物理与天体物理 Q1 Physics and Astronomy

Progress of Theoretical and Experimental Physics Pub Date : 2024-02-07 DOI:10.1093/ptep/ptae018

Shinsuke Nishigaki

引用次数: 0

Abstract

Motivated by the study of Polyakov lines in gauge theories, Hanada and Watanabe Hanada and Watanabe [1] recently presented a conjectured formula for the distribution of eigenphases of Haar-distributed random SU(N) matrices (β = 2), supported by explicit examples at small N and by numerical samplings at larger N. In this letter, I spell out a concise proof of their formula, and present its orthogonal and symplectic counterparts, i.e. the eigenphase distributions of Haar-random unimodular symmetric (β = 1) and selfdual (β = 4) unitary matrices parametrizing SU(N)/SO(N) and SU(2N)/Sp(2N), respectively.

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单模块圆形集合的特征相分布

受规规理论中波利亚科夫线研究的启发，Hanada 和 Watanabe Hanada 和 Watanabe [1] 最近提出了哈尔分布随机 SU(N) 矩阵 (β = 2) 的特征相分布的猜想公式，并得到了小 N 时的明确示例和大 N 时的数值采样的支持。在这封信中，我简明扼要地证明了他们的公式，并提出了其正交和交错对应公式，即分别参数化 SU(N)/SO(N) 和 SU(2N)/Sp(2N) 的哈尔随机单模态对称矩阵 (β = 1) 和自偶矩阵 (β = 4) 的特征相分布。

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

Progress of Theoretical and Experimental Physics PHYSICS, MULTIDISCIPLINARY-PHYSICS, PARTICLES & FIELDS

CiteScore

12.00

自引率

5.70%

发文量

148

审稿时长

17 weeks

期刊介绍： Progress of Theoretical and Experimental Physics (PTEP) is an international journal that publishes articles on theoretical and experimental physics. PTEP is a fully open access, online-only journal published by the Physical Society of Japan. PTEP is the successor to Progress of Theoretical Physics (PTP), which terminated in December 2012 and merged into PTEP in January 2013. PTP was founded in 1946 by Hideki Yukawa, the first Japanese Nobel Laureate. PTEP, the successor journal to PTP, has a broader scope than that of PTP covering both theoretical and experimental physics. PTEP mainly covers areas including particles and fields, nuclear physics, astrophysics and cosmology, beam physics and instrumentation, and general and mathematical physics.