Phonon relaxation and heat conduction in one-dimensional Fermi Pasta Ulam β lattices by molecular dynamics simulations  

作　　者：Hou Quan-Wen Cao Bing-Yang 侯泉文;曹炳阳(Key Laboratory for Thermal Science and Power Engineering of Ministry of Education,Department of Engineering Mechanics,Tsinghua University,Beijing 100084,China;Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education,Department of Applied Physics,Northwestern Polytechnical University,Xi’an 710072,China)

机构地区：[1]Key Laboratory for Thermal Science and Power Engineering of Ministry of Education,Department of Engineering Mechanics,Tsinghua University,Beijing 100084,China [2]Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education,Department of Applied Physics,Northwestern Polytechnical University,Xi’an 710072,China

出　　处：《Chinese Physics B》2012年第1期279-283,共5页中国物理B（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Grant Nos.50976052,51136001,and 50730006);the Program for New Century Excellent Talents in University,China;the Tsinghua University Initiative Scientific Research Program,China;the Tsinghua National Laboratory for Information Science and Technology TNList Cross-discipline Foundation,China

摘　　要：The phonon relaxation and heat conduction in one-dimensional Fermi Pasta-Ulam （FPU） β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autoeorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k^1.688, which leads to a N^0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N^2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.The phonon relaxation and heat conduction in one-dimensional Fermi Pasta-Ulam （FPU） β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autoeorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k^1.688, which leads to a N^0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N^2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.

关 键 词：thermal conductivity phonon relaxation low-dimensional heat conduction FermiPasta Ulam （FPU） Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education Department of Applied Physics Northwestern Polytechnical University Xi＇an 710072 China lattice 

分 类 号：O488[理学—固体物理]