具有长程相互作用正方晶格的色散关系和热容  

Dispersion Relations and Heat Capacity with Long Range Interactions in a Square Lattice

作　　者：李震东 谭振庭 方萍 LI Zhendong;TAN Zhenting;FANG Ping(School of Science,Beijing University of Posts and Telecommunications,Beijing 100876,China)

机构地区：[1]北京邮电大学理学院,北京100876

出　　处：《北京邮电大学学报》2022年第5期60-65,共6页Journal of Beijing University of Posts and Telecommunications

基　　金：国家自然科学基金项目(12005024);中央高校基本科研业务费专项资金项目(2020RC13,2021XD-A10)。

摘　　要：根据晶格动力学理论计算具有长程相互作用二维单原子正方晶格的色散关系,在简谐近似下,得到了考虑任意近邻原子色散关系的一般表达式。分析了最近邻和次近邻近似下的结果,当近邻数p较大时,第p近邻的原子对第一布里渊区内平均振动频率的贡献随近邻数的增大以幂律形式衰减。以长程库仑相互作用为例,进行数值计算和分析。在此微观动力学的基础上,研究了长程相互作用对宏观热容的影响。数值计算长程库仑相互作用系统的热容,且发现热容随近邻数的增大以幂律形式衰减。The dispersion relation of a monoatomic two-dimensional lattice with long-range interactions is derived according to the theory of lattice dynamics.Based on a simple harmonic approximation,a general dispersion relation that takes into account arbitrary neighbor interactions is obtained.The results of the nearest neighbor and the second nearest neighbor approximation are analyzed.When the order of the nearest neighbors p is large,the contribution of the pnearest neighbors to the average vibration frequency in the Brillouin zone decays in a power law form with the increase of the neighbor number.Moreover,the long-range Coulomb interaction is analyzed as an example.Based on this microscopic dynamics,the effect of long-range interaction on macroscopic heat capacity is numerically investigated,and the heat capacity of the system decays in a power law form with the increase of the neighbor number.

关 键 词：晶格振动 色散关系 简谐近似 周期性边界条件 正方晶格 热容 

分 类 号：TN301[电子电信—物理电子学]