Krylov Complexity in Mixed Phase Space
Abstract
We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans two-dimensional random matrix models featuring (I) GOE-Poisson and (II) GUE-Poisson transitions and extends to higher-dimensional cases, including a stringy matrix model (GOE-Poisson) and the mass-deformed SYK model (GUE-Poisson). Krylov complexity consistently emerges as a reliable marker of quantum chaos, displaying a characteristic peak in the chaotic regime that gradually diminishes as the Brody parameter approaches zero, signaling a shift toward integrability. These results establish Krylov complexity as a powerful diagnostic of quantum chaos and highlight its interplay with eigenvalue statistics in mixed phase systems.
Keywords
Cite
@article{arxiv.2412.04963,
title = {Krylov Complexity in Mixed Phase Space},
author = {Kyoung-Bum Huh and Hyun-Sik Jeong and Leopoldo A. Pando Zayas and Juan F. Pedraza},
journal= {arXiv preprint arXiv:2412.04963},
year = {2025}
}
Comments
v1: 10 pages, 16 figures, v2 : references added, minor changes, v3: matching the published version