宏观弱不可积映射的热化动力学
Thermalization dynamics of macroscopic weakly nonintegrable maps
摘要：
研究了弱不可积非线性幺正格点动力学的热化问题。我们确定了两个不同的热化制度接近的可积极限的线性动力学或断开晶格动力学。对于弱非线性，几乎守恒作用对应于耦合到长程网络中的扩展可观测量。对于弱连通格点，相应的局部观测量被耦合到一个短程网络中。我们计算的方差$σ^2(T)$的有限时间平均分布的扩展和本地的可观测量的演变。我们提取遍历时间尺度$T_E$，它标志着热化的开始，并通过随后的衰减$σ^2(T)$确定网络的类型。我们利用李雅普诺夫谱的互补分析[M. Malishava和S. Flach，Phys. Rev. Lett. 128，134102（2022）]并将李雅普诺夫时间$T_Λ$与$T_E$进行比较。我们刻画了切向量的空间性质，得到了弱不可积宏观热化动力学的完整分类图。
英文摘要：
We study thermalization of weakly nonintegrable nonlinear unitary lattice dynamics. We identify two distinct thermalization regimes close to the integrable limits of either linear dynamics or disconnected lattice dynamics. For weak nonlinearity the almost conserved actions correspond to extended observables which are coupled into a long-range network. For weakly connected lattices the corresponding local observables are coupled into a short-range network. We compute the evolution of the variance $σ^2(T)$ of finite time average distributions for extended and local observables. We extract the ergodization time scale $T_E$ which marks the onset of thermalization, and determine the type of network through the subsequent decay of $σ^2(T)$. We use the complementary analysis of Lyapunov spectra [M. Malishava and S. Flach, Phys. Rev. Lett. 128, 134102 (2022)] and compare the Lyapunov time $T_Λ$ with $T_E$. We characterize the spatial properties of the tangent vector and arrive at a complete classification picture of weakly nonintegrable macroscopic thermalization dynamics.
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