Nonlinear dynamics in fractal structures

点击翻译按钮获取中文摘要

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