Malishava Merab, Flach Sergej
Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34126, South Korea.
Chaos. 2022 Jun;32(6):063113. doi: 10.1063/5.0092032.
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 ( T ) of finite time average distributions for extended and local observables. We extract the ergodization time scale which marks the onset of thermalization, and determine the type of network through the subsequent decay of ( 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 with . We characterize the spatial properties of the tangent vector and arrive at a complete classification picture of weakly nonintegrable macroscopic thermalization dynamics.
我们研究弱非可积非线性幺正晶格动力学的热化问题。我们确定了两种不同的热化区域，它们接近线性动力学或非连通晶格动力学的可积极限。对于弱非线性，几乎守恒的作用量对应于扩展可观测量，这些可观测量耦合到一个长程网络中。对于弱连通晶格，相应的局部可观测量耦合到一个短程网络中。我们计算了扩展和局部可观测量的有限时间平均分布的方差(\varDelta(T))的演化。我们提取了标志热化开始的遍历化时间尺度(\tau)，并通过(\varDelta(T))随后的衰减来确定网络的类型。我们使用李雅普诺夫谱的互补分析[M. 马利沙瓦和S. 弗拉赫，《物理评论快报》128, 134102 (2022)]，并将李雅普诺夫时间(T_{Ly})与(\tau)进行比较。我们刻画了切向量的空间性质，并得出了弱非可积宏观热化动力学的完整分类图景。
