Nonlinear dynamics in fractal structures

本项目的目的是阐明在具有分形结构的网络玻璃、聚合物、凝胶聚集体中观察到的各种独特现象，特别是关于在低温下观察到的强局域模之间的非谐相互作用引起的跳跃电导率。玻璃在几个方面不同于没有内部应变的通常随机介质，并且不处于热平衡。在聚合物、网络形成玻璃和凝胶中观察到的热导率kappa（T）表现出普遍的行为，如在几开尔文以下的T^2依赖性和在10 K左右的平台。我们阐明了kappa（T）的平台可以用玻璃中声子的迁移率边缘的存在来解释。在约10- 30 K的平台的高温端，观察到kappa（T）随温度T的升高而升高。我们已经定量地表明，kappa（T）的升高至少在初始时与I成线性关系，可以用跳跃机制来解释，即，我们有 ...更多信息 建议存在一个额外的热传导通道，这可以通过在相关温度下将玻璃中的振动态的一般特征结合起来解释。此外，我们还阐明了在网络形成玻璃的拉曼和中子散射实验中观察到的30 - 50 cm ~ 2附近的玻色子峰<-1>与热导率的平台区具有相同的起源。第二，我们指出具有大的非谐性的局部畸变势在产生声学带中的强局域模中起作用。最后，我们已经成功地定量解释了大的非谐性是强局域模的跳跃输运的原因，这导致了一致的解释平台和随后的单调增加的平台温度以上的k。我们的分析将阐明新的长期存在的问题，在分形结构和玻璃中观察到的各种独特和普遍的属性。少

The purpose of this project is to clarify various unique phenomena observed in network glasses, polymers, gel-aggragates taking fractal structures, in particular about the hopping conductivities due to anharmonic interaction between strongly localized modes observed at low temperatures. Glasses are different in several aspects from usual random media without internal strain and are not in thermal equilibrium. Thermal conductivities kappa(T) observed in polymers, network-forming glasses, and gelaggragates show universal behaviors such as the T^2-dependence below a few Kelvin and the plateau at around 10K.We have clarified that the plateau in kappa(T) can be explained by the existence of a mobility edge for phonons in glasses. At the high-temperature end of the plateau at around 10-30K, kappa(T) observed rise with increasing temperature T.We have shown quantitatively that the rise of kappa(T) certainly at least initially linear on I can be explained the hopping mechanism, namely, we have … More suggested the existence of an additional heat conduction channel, which can be explained by incorporating generic features of vibrational states in glasses at relevant temperatures. In addition, we have clarified in this project that the boson peak in the vicinity of 3O-50cm^<-1> observed in Raman and neutron scattering experiments for network-forming glasses has the same origin as the plateau region in thermal conductivities, In the second, we have pointed out that locally distorted potentials with large anharmonicities play a role in creating strongly localized modes in the acoustic band. Finally, we have succeeded to quantitatively explain that the large anharmonicity is the cause of the hopping transport of strongly localized modes, which leads a consistent explanation of the plateau and the subsequent monotonic increase of k above the plateau temperature. Our analysis will shed new light on the elucidation of long-standing problem on various unique and universal properties observed in fractal structures and glasses. Less