固定边界条件下Fermi-Pasta-Ulam-Tsingou短链能量均分性质研究  

Energy equipartition properties of Fermi-Pasta-Ulam-Tsingou system for small number of particles with fixed boundary conditions

作　　者：鲁明亮[1] 张振俊[2] 苑晓丽 LU Ming-Liang;ZHANG Zhen-Jun;YUAN Xiao-Li(Nanjing Branch of Jiangsu Union Technical Institute,Nanjing 210019,China;College of Science,Hohai University,Nanjing 210098,China)

机构地区：[1]江苏联合职业技术学院南京分院,南京210019 [2]河海大学理学院,南京210098

出　　处：《原子与分子物理学报》2023年第3期145-150,共6页Journal of Atomic and Molecular Physics

基　　金：中央高校业务经费专项基金(B210202148);省级农业科技创新与推广专项(NJ2021-21)。

摘　　要：采用固定边界条件,数值研究了Fermi-Pasta-Ulam-Tsingou(FPUT)短链的能量均分性质.研究发现,在较强的非线性强度区间内,能量均分时间t_(eq)与能量密度ε满足t_(eq)~ε^(-4.0)的标度关系.在该非线性强度区间内,能量通过相邻本征模之间的共振不停的传输,并最终达到能量均分状态.这说明,即使不存在非平庸的六波共振,只要相邻本征模间的共振可以发生,t_(eq)~ε^(-4.0)的标度关系就能出现.随着非线性强度的减小,该标度关系不再成立.此时,能量是通过高频本征模的共振逐渐向低频本征模传输的.The properties of energy equipartition in Fermi-Pasta-Ulam-Tsingou(FPUT)system using fixed boundary conditions for small number of particles are studied.Energy equipartition time t_(eq)depending on system’s energy densityεshows a power law scaling t_(eq)~ε^(-4.0)within a certain range of nonlinearity.In this range of nonlinearity,energies can interchange between the adjacent eigenmodes continuously with time through the mechanism of overlap of frequencies until reaching the energy equipartition state.It suggests that even if there are no nontrivial six-wave resonances,as long as the resonances between adjacent eigenmodes occur,the power law t_(eq)~ε^(-4.0)will appear.With a further decreasing nonlinearity,there will be a steeper growth than t_(eq)~ε^(-4.0).In this range of nonlinearity,energy transport process is found to be related with the resonances of high frequency modes.

关 键 词：FPUT短链 固定边界条件 能量均分 共振 

分 类 号：O415.6[理学—理论物理]