Work

Krylov complexity in mixed phase space

Year: 2025

Type: article

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.

Source: Physical review. D/Physical review. D.

DOI: 10.1103/gmy7-dn7l

Authors: Kyoung-Bum Huh, Hyun-Sik Jeong, Leopoldo A. Pando Zayas, Juan F. Pedraza

Institutions: Shanghai Jiao Tong University, Instituto de Física Teórica, The Abdus Salam International Centre for Theoretical Physics (ICTP), University of Michigan

Language: English

Topic: Quantum chaos and dynamical systems

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid