1. Observation of prethermalization in weakly nonintegrable unitary maps
- Author
-
Zhang, Xiaodong, Lando, Gabriel M., Dietz, Barbara, and Flach, Sergej
- Subjects
Nonlinear Sciences - Chaotic Dynamics ,Condensed Matter - Statistical Mechanics - Abstract
We investigate prethermalization by studying the statistical properties of the time-dependent largest Lyapunov exponent $\Lambda(t)$ for unitary-circuit maps upon approaching integrability. We follow the evolution of trajectories for different initial conditions and compute the mean $\mu(t)$ and standard deviation $\sigma(t)$ of $\Lambda(t)$. Thermalization implies a temporal decay $\sigma \sim t^{-1/2}$ at a converged finite value of $\mu$. We report prethermalization plateaus that persist for long times where both $\mu$ and $\sigma$ appear to have converged to finite values, seemingly implying differing saturated Lyapunov exponent values for different trajectories. The lifetime of such plateaus furnishes a novel time scale characterizing the thermalization dynamics of many-body systems close to integrability. We also find that the plateaus converge to their respective thermal values for long enough times., Comment: Dedicated to Professor Alexander Kovalev from B. Verkin Institute for Low Temperature Physics and Engineering of the NASU (Kharkiv, Ukraine) on the occasion of his 80th birthday
- Published
- 2025