准周期非线性酉矩阵的李雅普诺夫谱标度转变
Lyapunov spectrum scaling transition for quasiperiodic nonlinear unitaries
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中文总结 AI 辅助
研究准周期势下热弱非线性酉映射的李雅普诺夫谱标度转变，通过与安德森无序比较，发现准周期性虽增强局域化影响，但标度转变强烈延迟，揭示了准周期局域本征态长程关联的潜在影响。
中文摘要 AI 辅助
我们研究了在准周期势存在下热弱非线性酉映射的李雅普诺夫谱标度。随着局域长度ξ减小，我们寻找从长程到短程标度的转变，并将细节与不相关安德森无序情况进行比较。线性情况本征态的比较统计分析表明，在相同ξ值下准周期性具有更强的局域化影响，预计标度转变也会增强。然而，数值分析表明它比安德森无序强烈延迟，在异常小的ξ值时才观察到。这些发现暗示了准周期局域本征态长程关联的潜在影响，即使在可积性破坏和热化情况下相互作用存在时也持续存在。
英文摘要
We study the Lyapunov spectrum scaling of thermal weakly-nonlinear unitary maps in the presence of quasiperiodic potentials. We search for the crossover from long-range to short-range scaling as the localization length ξ decreases and compare the details to the case of uncorrelated Anderson disorder [Phys. Rev. Res. 6 L012064 (2024)]. A comparative statistical analysis of the eigenstates for the linear case shows that quasiperiodicity has a stronger localization impact at the same value of ξ. Therefore we expect that the scaling crossover should be enhanced as well. However, the numerical analysis shows that it is strongly delayed as compared to Anderson disorder, and is observed at anomalously small values of ξ. These findings hint at the potential impact of long range correlations of quasiperiodic localized eigenstates, which persist in the presence of interactions even in the case of integrability breaking and thermalization.
