OAK

Spectral and Krylov complexity in billiard systems

Metadata Downloads
Abstract
In this work, we investigate spectral complexity and Krylov complexity in quantum billiard systems at finite temperature. We study both circle and stadium billiards as paradigmatic examples of integrable and nonintegrable quantum-mechanical systems, respectively. We show that the saturation value and timescale of spectral complexity may be used to probe the nonintegrability of the system since we find that when computed for the circle billiard, it saturates at a later timescale compared to the stadium billiards. This observation is verified for different temperatures. Furthermore, we study the Krylov complexity of the position operator and its associated Lanczos coefficients at finite temperature using the Wightman inner product. We find that the growth rate of the Lanczos coefficients saturates the conjectured universal bound at low temperatures. Additionally, we also find that even a subset of the Lanczos coefficients can potentially serve as an indicator of integrability, as they demonstrate erratic behavior specifically in the circle billiard case, in contrast to the stadium billiard. Finally, we also study Krylov entropy and verify its early-time logarithmic relation with Krylov complexity in both types of billiard systems. © 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the https://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.
Author(s)
Camargo, Hugo A.Jahnke, ViktorJeong, Hyun-SikKim, Keun-YoungNishida, Mitsuhiro
Issued Date
2024-02
Type
Article
DOI
10.1103/PhysRevD.109.046017
URI
https://scholar.gist.ac.kr/handle/local/9717
Publisher
American Physical Society
Citation
Physical Review D, v.109, no.4
ISSN
2470-0010
Appears in Collections:
Department of Physics and Photon Science > 1. Journal Articles
공개 및 라이선스
  • 공개 구분공개
파일 목록
  • 관련 파일이 존재하지 않습니다.

Items in Repository are protected by copyright, with all rights reserved, unless otherwise indicated.