Mulansky Mario, Pikovsky Arkady
Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Strasse 24, D-14476 Potsdam-Golm, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056214. doi: 10.1103/PhysRevE.86.056214. Epub 2012 Nov 26.
In nonlinear disordered Hamiltonian lattices, where there are no propagating phonons, the spreading of energy is of subdiffusive nature. Recently, the universality class of the subdiffusive spreading according to the nonlinear diffusion equation (NDE) has been suggested and checked for one-dimensional lattices. Here, we apply this approach to two-dimensional strongly nonlinear lattices and find a nice agreement of the scaling predicted from the NDE with the spreading results from extensive numerical studies. Moreover, we show that the scaling works also for regular lattices with strongly nonlinear coupling, for which the scaling exponent is estimated analytically. This shows that the process of chaotic diffusion in such lattices does not require disorder.
在不存在传播声子的非线性无序哈密顿晶格中，能量的扩散具有亚扩散性质。最近，有人提出并针对一维晶格检验了根据非线性扩散方程（NDE）得到的亚扩散扩散的普适类。在此，我们将此方法应用于二维强非线性晶格，并发现NDE预测的标度与大量数值研究的扩散结果吻合良好。此外，我们表明该标度对于具有强非线性耦合的规则晶格也适用，其标度指数可通过解析方法估算。这表明此类晶格中的混沌扩散过程并不需要无序。
