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arXiv · 2501.07956

Observation of prethermalization in weakly nonintegrable unitary maps

Xiaodong Zhang·Gabriel M. Lando·Barbara Dietz·Sergej Flach
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Abstract

We investigate prethermalization by studying the statistical properties of the time-dependent largest Lyapunov exponent $Λ(t)$ for unitary-circuit maps upon approaching integrability. We follow the evolution of trajectories for different initial conditions and compute the mean $μ(t)$ and standard deviation $σ(t)$ of $Λ(t)$. Thermalization implies a temporal decay $σ\sim t^{-1/2}$ at a converged finite value of $μ$. We report prethermalization plateaus that persist for long times where both $μ$ and $σ$ 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.

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Xiaodong Zhang, Gabriel M. Lando, Barbara Dietz, Sergej Flach. 2025-01-14. Observation of prethermalization in weakly nonintegrable unitary maps. https://arxiv.org/abs/2501.07956

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