Cui Bingyu, Milkus Rico, Zaccone Alessio
Statistical Physics Group, Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Cambridge CB2 3RA, United Kingdom.
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Phys Rev E. 2017 Feb;95(2-1):022603. doi: 10.1103/PhysRevE.95.022603. Epub 2017 Feb 10.
We compute the dielectric response of glasses starting from a microscopic system-bath Hamiltonian of the Zwanzig-Caldeira-Leggett type and using an ansatz from kinetic theory for the memory function in the resulting generalized Langevin equation. The resulting framework requires the knowledge of the vibrational density of states (DOS) as input, which we take from numerical evaluation of a marginally stable harmonic disordered lattice, featuring a strong boson peak (excess of soft modes over Debye ∼ω_{p}^{2} law). The dielectric function calculated based on this ansatz is compared with experimental data for the paradigmatic case of glycerol at T≲T_{g}. Good agreement is found for both the reactive (real) part of the response and for the α-relaxation peak in the imaginary part, with a significant improvement over earlier theoretical approaches. On the low-frequency side of the α peak, the fitting supports the presence of ∼ω_{p}^{4} modes at vanishing eigenfrequency as recently shown [E. Lerner, G. During, and E. Bouchbinder, Phys. Rev. Lett. 117, 035501 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.035501]. α-wing asymmetry and stretched-exponential behavior are recovered by our framework, which shows that these features are, to a large extent, caused by the soft boson-peak modes in the DOS.
我们从Zwanzig-Caldeira-Leggett型微观系统-浴哈密顿量出发，并在所得广义朗之万方程中使用动力学理论的一个假设来计算玻璃的介电响应。由此产生的框架需要以振动态密度（DOS）的知识作为输入，我们从一个略微稳定的谐波无序晶格的数值评估中获取该知识，该晶格具有一个强玻色子峰（软模超过德拜ω_p^2定律的过量部分）。基于此假设计算的介电函数与甘油在T≲T_g的典型情况下的实验数据进行了比较。在响应的实部（有功部分）和虚部的α弛豫峰方面都发现了很好的一致性，与早期理论方法相比有显著改进。在α峰的低频侧，拟合支持了最近所显示的在本征频率为零时ω_p^4模式的存在[E. Lerner, G. During, and E. Bouchbinder, Phys. Rev. Lett. 117, 035501 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.035501]。我们的框架恢复了α翼不对称性和拉伸指数行为，这表明这些特征在很大程度上是由DOS中的软玻色子峰模式引起的。
