标题： 调和晶体中多原子晶格的热平衡方法 显示英文标题

标题： Approach to thermal equilibrium in harmonic crystals with polyatomic lattice

摘要： 我们研究无限谐波晶体中复杂的（多原子）晶格中的瞬态热过程。初始时粒子的位移为零，速度是随机的，使得温度分布在空间上是均匀的。初始的动能和势能不同，因此系统远离热平衡。研究了对应于原胞不同自由度的动能温度的时间演化。结果表明，温度随时间振荡，并趋于通常不同的平衡值。这些振荡是由两种物理过程引起的：动能和势能的平衡以及原胞内自由度之间温度的重新分布。得到了描述这些振荡的精确公式。在长时间后，晶体接近热平衡，即温度随时间保持恒定的状态。推导了温度平衡值与初始条件之间的关系。这种关系被称为非均分定理。为了说明，考虑了双原子链和石墨烯晶格中的瞬态热过程。解析结果由晶格动力学方程的数值解支持。${\bf Keywords}$: 热平衡；稳态；趋向平衡；多原子晶格；复杂晶格；动能温度；谐波晶体；瞬态过程；均分定理；温度矩阵。 显示英文摘要

摘要： We study transient thermal processes in infinite harmonic crystals with complex (polyatomic) lattice. Initially particles have zero displacements and random velocities such that distribution of temperature is spatially uniform. Initial kinetic and potential energies are different and therefore the system is far from thermal equilibrium. Time evolution of kinetic temperatures, corresponding to different degrees of freedom of the unit cell, is investigated. It is shown that the temperatures oscillate in time and tend to generally different equilibrium values. The oscillations are caused by two physical processes: equilibration of kinetic and potential energies and redistribution of temperature among degrees of freedom of the unit cell. An exact formula describing these oscillations is obtained. At large times, a crystal approaches thermal equilibrium, i.e. a state in which the temperatures are constant in time. A relation between equilibrium values of the temperatures and initial conditions is derived. This relation is refereed to as the non-equipartition theorem. For illustration, transient thermal processes in a diatomic chain and graphene lattice are considered. Analytical results are supported by numerical solution of lattice dynamics equations. ${\bf Keywords}$: thermal equilibrium; stationary state; approach to equilibrium; polyatomic lattice; complex lattice; kinetic temperature; harmonic crystal; transient processes; equipartition theorem; temperature matrix.