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

doi:10.1088/1674-1056/21/1/014401

中国物理B ›› 2012, Vol. 21 ›› Issue (1): 14401-014401.doi: 10.1088/1674-1056/21/1/014401

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

曹炳阳¹, 侯泉文²

(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 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

收稿日期:2011-06-12 修回日期:2011-09-13 出版日期:2012-01-15 发布日期:2012-01-20
基金资助:
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,

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

Hou Quan-Wen(侯泉文)^a)b) and Cao Bing-Yang(曹炳阳)^a)^†

^a Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China; ^b Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education, Department of Applied Physics, Northwestern Polytechnical University, Xi’an 710072, China

Received:2011-06-12 Revised:2011-09-13 Online:2012-01-15 Published:2012-01-20
Supported by:
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,

摘要/Abstract

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 autocorrelation 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, Fermi-Pasta-Ulam (FPU) β lattice

Abstract: 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 autocorrelation 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.

Key words: thermal conductivity, phonon relaxation, low-dimensional heat conduction, Fermi-Pasta-Ulam (FPU) β lattice

中图分类号: (Heat conduction)

44.10.+i

63.22.-m (Phonons or vibrational states in low-dimensional structures and nanoscale materials) 66.25.+g (Thermal conduction in nonmetallic liquids)

侯泉文, 曹炳阳. Phonon relaxation and heat conduction in one-dimensional Fermi–Pasta–Ulam β lattices by molecular dynamics simulations[J]. 中国物理B, 2012, 21(1): 14401-014401.

Hou Quan-Wen(侯泉文) and Cao Bing-Yang(曹炳阳) . Phonon relaxation and heat conduction in one-dimensional Fermi–Pasta–Ulam β lattices by molecular dynamics simulations[J]. Chin. Phys. B, 2012, 21(1): 14401-014401.

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

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

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