2025/01/14 by Xiaodong Zhang, Gabriel M. Lando, Zhang, Xiaodong +5 · 2 citations
Mathematics · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Statistical Mechanics (cond-mat.stat-mech) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2501.07956
openalex publication_date 2025/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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∼ 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.