Anomalous diffusion is simulated in this paper by studying the transport of discrete solitons in a lattice with evolving disorder. We find a Richardson-type diffusion for the small solitons and a regime of transient diffusion for larger solitons within the ensemble-averaged description. As a comparison, the time-averaged observables present a ballistic scaling for both cases. However, distribution of these observables changes remarkably with the soliton size. Our results suggest violation of ergodicity for the solitons' diffusive processes, which are expected to shed light on further understanding of the discreteness-disorder-nonlinearity interaction.

中文翻译：

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由进化紊乱驱动的离散孤子的异常扩散。

通过研究离散的孤子在具有无序演化的晶格中的输运，来模拟异常扩散。在整体平均描述中，我们发现了小孤子的Richardson型扩散和大孤子的瞬态扩散状态。作为比较，两种情况下的时间平均观测值都具有弹道缩放比例。但是，这些可观察物的分布随孤子尺寸而显着变化。我们的研究结果表明，孤子的扩散过程违反了遍历性，这有望进一步阐明离散性，无序性，非线性相互作用。