Miserez Florian, Ganguly Saswati, Haussmann Rudolf, Fuchs Matthias
Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany.
Phys Rev E. 2022 Nov;106(5-1):054125. doi: 10.1103/PhysRevE.106.054125.
We present a microscopic derivation of the laws of continuum mechanics of nonideal ordered solids including dissipation, defect diffusion, and heat transport. The starting point is the classical many-body Hamiltonian. The approach relies on the Zwanzig-Mori projection operator formalism to connect microscopic fluctuations to thermodynamic derivatives and transport coefficients. Conservation laws and spontaneous symmetry breaking, implemented via Bogoliubov's inequality, determine the selection of the slow variables. Density fluctuations in reciprocal space encode the displacement field and the defect concentration. Isothermal and adiabatic elastic constants are obtained from equilibrium correlations, while transport coefficients are given as Green-Kubo formulas, providing the basis for their measurement in atomistic simulations or colloidal experiments. The approach to the linearized continuum mechanics and results are compared to others from the literature.
我们给出了非理想有序固体连续介质力学定律的微观推导，其中包括耗散、缺陷扩散和热输运。出发点是经典的多体哈密顿量。该方法依赖于兹万齐格 - 莫里投影算符形式，以将微观涨落与热力学导数及输运系数联系起来。通过博戈留波夫不等式实现的守恒定律和自发对称性破缺，决定了慢变量的选择。倒易空间中的密度涨落编码了位移场和缺陷浓度。等温及绝热弹性常数由平衡关联得到，而输运系数则以格林 - 库博公式给出，为在原子模拟或胶体实验中测量它们提供了基础。将线性化连续介质力学的方法及结果与文献中的其他方法进行了比较。
