Observation of prethermalization in weakly nonintegrable unitary maps

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.

arXiv commentDedicated 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