Nonlinear dynamics in fractal structures

本项目的目的是澄清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，特别是在低温下观察到的强局域模式之间的非调和相互作用引起的跳变电导率。玻璃在许多方面不同于通常的无内部应变和非热平衡的随机介质。在聚合物、网状玻璃和凝胶团块中观察到的热导率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10K左右的平台。我们已经澄清了kappa(T)中的平台可以用玻璃中声子的迁移率边缘的存在来解释。在高原的高温末端，在10-30K左右，kappa(T)随温度T的升高而升高。我们已经定量地表明，kappa(T)的升高至少在最初是线性的，可以解释跳跃机制，即，我们有…More提出了一个额外的热传导通道的存在，这可以通过结合玻璃在相关温度下振动态的一般特征来解释。此外，我们在本项目中澄清了在网络形成玻璃的拉曼和中子散射实验中观察到的30 -50cm^<-1>附近的玻色子峰与热导率的平台区具有相同的起源。其次，我们指出了具有大不谐性的局部扭曲势在声带中产生强局域模式中起作用。最后，我们成功地定量地解释了大的非调和性是强局域模式跳变输运的原因，这导致了高原和随后的高原温度以上k单调增加的一致解释。我们的分析将为阐明在分形结构和玻璃中观察到的各种独特和普遍性质的长期问题提供新的线索。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