Instituto de Fisica Teorica UAM/CSIC, Universidad Autonoma de Madrid, Cantoblanco, 28049 Madrid, Spain.
Physik-Department, Technical University Munich, James-Franck-Str. 1, 85748 Garching, Germany.
Phys Rev E. 2019 Dec;100(6-1):062131. doi: 10.1103/PhysRevE.100.062131.
The low-temperature properties of glasses present important differences with respect to crystalline matter. In particular, models such as the Debye model of solids, which assume the existence of an underlying regular lattice, predict that the specific heat of solids varies with the cube of temperature at low temperatures. Since the 1970s at least, it is a well-established experimental fact that the specific heat of glasses is instead just linear in T at T∼1 K and presents a pronounced peak when normalized by T^{3}, known as the boson peak. Here we present an approach which suggests that the vibrational and thermal properties of amorphous solids are affected by the random-matrix part of the vibrational spectrum. The model is also able to reproduce, for the first time, the experimentally observed inverse proportionality between the boson peak in the specific heat and the shear modulus.
玻璃的低温性质与晶体物质有重要的区别。特别是，像固体德拜模型这样的模型，假设存在一个基础的规则晶格，预测固体的比热容随低温下温度的立方而变化。至少从 20 世纪 70 年代开始，一个被广泛证实的实验事实是，玻璃的比热容在 T∼1 K 时与 T 呈线性关系，并且当按 T^{3}归一化时呈现出明显的峰值，称为玻色峰。在这里，我们提出了一种方法，表明无定形固体的振动和热性质受到振动谱的随机矩阵部分的影响。该模型还首次能够再现实验观察到的比热中的玻色峰与剪切模量之间的反比关系。
