Abstract

Thermal vibrations in a d-dimensional (d = 1, 2) scalar harmonic lattice of a simple structure are under consideration. Redistribution of the averaged kinetic and potential energies of particles after instantaneous thermal excitation (fast process) is described. It is established that the difference between the kinetic and potential energies undergoes power-law damped oscillations at times much longer than the characteristic atomic-vibration period. A typical exponent is –d/2. The oscillation frequencies are determined from the dispersion relation for the lattice. The algorithm of proving allows generalization to scalar and vector lattices with a complex structure and different dimensions. Thermal vibrations in a two-dimensional hexagonal lattice (graphene lattice) are considered as an example of this generalization.

中文翻译：

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标量谐波晶格中快速热过程的渐近描述

摘要

正在考虑简单结构的d维（d = 1，2）标量谐波晶格中的热振动。描述了瞬时热激发（快速过程）后颗粒平均动能和势能的重新分布。可以确定的是，动能和势能之间的差会经历比幂原子振动周期长得多的幂律阻尼振荡。典型的指数是– d/ 2。振荡频率由晶格的色散关系确定。证明算法允许泛化具有复杂结构和不同维度的标量和矢量晶格。二维六角形晶格（石墨烯晶格）中的热振动被认为是这种概括的一个例子。