二维无序非线性晶格中的混沌波包扩展
Chaotic wave-packet spreading in two-dimensional disordered nonlinear lattices.
作者信息
Many Manda B, Senyange B, Skokos Ch
机构信息
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, 7701 Cape Town, South Africa.
出版信息
Phys Rev E. 2020 Mar;101(3-1):032206. doi: 10.1103/PhysRevE.101.032206.
We reveal the generic characteristics of wave-packet delocalization in two-dimensional nonlinear disordered lattices by performing extensive numerical simulations in two basic disordered models: the Klein-Gordon system and the discrete nonlinear Schrödinger equation. We find that in both models (a) the wave packet's second moment asymptotically evolves as t^{a_{m}} with a_{m}≈1/5 (1/3) for the weak (strong) chaos dynamical regime, in agreement with previous theoretical predictions [S. Flach, Chem. Phys. 375, 548 (2010)CMPHC20301-010410.1016/j.chemphys.2010.02.022]; (b) chaos persists, but its strength decreases in time t since the finite-time maximum Lyapunov exponent Λ decays as Λ∝t^{α_{Λ}}, with α_{Λ}≈-0.37 (-0.46) for the weak (strong) chaos case; and (c) the deviation vector distributions show the wandering of localized chaotic seeds in the lattice's excited part, which induces the wave packet's thermalization. We also propose a dimension-independent scaling between the wave packet's spreading and chaoticity, which allows the prediction of the obtained α_{Λ} values.
通过在两个基本无序模型（克莱因 - 戈登系统和离散非线性薛定谔方程）中进行广泛的数值模拟，我们揭示了二维非线性无序晶格中波包离域的一般特征。我们发现，在这两个模型中：（a）对于弱（强）混沌动力学区域，波包的二阶矩渐近地随(t^{a_{m}})演化，其中(a_{m}\approx1/5)（(1/3)），这与先前的理论预测一致 [S. Flach, Chem. Phys. 375, 548 (2010)CMPHC20301 - 010410.1016/j.chemphys.2010.02.022]；（b）混沌持续存在，但其强度随时间(t)减小，因为有限时间最大李雅普诺夫指数(\Lambda)随(\Lambda\propto t^{\alpha_{\Lambda}})衰减，对于弱（强）混沌情况，(\alpha_{\Lambda}\approx - 0.37)（(-0.46)）；并且（c）偏差向量分布显示了局部混沌种子在晶格激发部分的游走，这导致了波包的热化。我们还提出了波包扩展与混沌之间的与维度无关的标度关系，这使得能够预测所获得的(\alpha_{\Lambda})值。
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