含有格点势的一维Fibonacci链热传导性质的研究

徐慧; 崔麦玲; 马松山

doi:10.7498/aps.59.7266

摘要

用传输矩阵的方法,研究了格点势(on-site势)对一维Fibonacci链的热传导性质(透射系数、Lyapunov指数及热导率κ)的影响.研究结果表明:当固定原子质量比和力作用常数比时,随着格点势的增大,低频区域的透射系数减小,对应的Lyapunov指数增大,透射谱向高频方向移动.同时,格点势越大,同样大小的体系对应的κ越小,当格点势足够大时,κ会趋近零.在热导率κ对振动频率ω2作图中,κ呈现台阶式缓慢上升的趋势,且在高频

关键词:

Abstract

By making use of the method of transfer matrix, we study the behaviors of heat conduction in one-dimensional Fibonacci chain under the influence of on-site potential (including transmission coefficient, Lyapunov coefficient and heat conduction). The results show that, with the on-site potential increasing while fixing the ratios of atom mass and force constant, the transmission coefficient of the low-frequency region decreases, and the corresponding Lyapunov coefficient increases, and the transmission spectrum moves to the higher frequency region. Meanwhile, with the increasing of on-site potential, the heat conductivity of the system decreases. When the on-site potential is large enough, the thermal conductivity of the system will tend to zero. In the curve of κ-ω2, the thermal conductivity shows a slowly increasing trend in steps, and tends to a certain value in the high-frequency region.

Keywords:

作者及机构信息

1.
中南大学物理科学与技术学院,长沙 410083

基金项目: 中国高等学校博士点专项科研基金(批准号:20070533075)和湖南省科技计划(批准号:2009FJ3004)资助的课题.

Authors and contacts

1.
College of Physical Science and Technology, Central South University, Changsha 410083, China

参考文献

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[3]	Chaly A, Polyanov V, Zakharov V 2005 The Fifth International Conference on Power Transmission & Dist Ribution Technology Beijing October 12—14, 2005 p147
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[5]	Hatano T 1999 Phys. Rev. Lett. 59 R1
[6]	Li B, Zhao H, Hu B 2001 Phys. Rev. Lett. 86 63
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[8]	Narayan O, Ramaswamy S 2002 Phys. Rev. Lett. 89 200601
[9]	Giulio C, Joseph F, Franco V, William M V 1984 Phys. Rev. Lett. 52 1861
[10]	Prosen T, Robnik M 1992 J. Phys. A 25 3449
[11]	Hu B, Lei Y 2005 Chaos 15 015119
[12]	Savin A V, Gendelman O V 2003 Phys. Rev. E 67 041205
[13]	Tong P Q, Li B W, Hu B B 1999 Phys. Rev. B 59 8639
[14]	Rubin R J, Green W L 1971 Math. Phys. 12 1686
[15]	Lepris S, Livi R, Poiti A 1997 Phys. Rev. Lett. 78 1896
[16]	Kaburaki H, Machida M 1993 Phys. Lett. A 181 85
[17]	Hu B, Li B W, Zhao H 1998 Phys. Rev. E 57 2992
[18]	Shechtman D, Blech I, Gratias D 1984 Phys. Rev. Lett. 53 1951
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[20]	Enrique M 1999 Phys. Rev. B 61 10
[21]	Huang X Q, Gong C D 1998 Phys. Rev. B 58 739
[22]	Bellisard J, Iochum B, Scoppola E, Testard D 1989 Math. Phys. 125 527
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施引文献

[1]	Lin S 2003 Permanent Magnetism Organization and Vacuum Breaker (Beijing: Mechanical Industry Press) (in Chinese)[林莘 2003 永磁机构与真空断路器 (北京: 机械工业出版社)]
[2]	Li J J 2005 Pragmatic Technology of High School Pressure Switch Equipment (Beijing: Mechanical Industry Press) (in Chinese) [李建基 2005 高中压开关设备实用技术 (北京: 机械工业出版社) ]
[3]	Chaly A, Polyanov V, Zakharov V 2005 The Fifth International Conference on Power Transmission & Dist Ribution Technology Beijing October 12—14, 2005 p147
[4]	Lepri S, Livi R, Politi A 1997 Phys. Rev. Lett. 78 1896
[5]	Hatano T 1999 Phys. Rev. Lett. 59 R1
[6]	Li B, Zhao H, Hu B 2001 Phys. Rev. Lett. 86 63
[7]	Li X X, Tang Y 2006 Acta Phys. Sin. 55 6556(in Chinese)[李新霞、唐翌 2006 物理学报 55 6556]
[8]	Narayan O, Ramaswamy S 2002 Phys. Rev. Lett. 89 200601
[9]	Giulio C, Joseph F, Franco V, William M V 1984 Phys. Rev. Lett. 52 1861
[10]	Prosen T, Robnik M 1992 J. Phys. A 25 3449
[11]	Hu B, Lei Y 2005 Chaos 15 015119
[12]	Savin A V, Gendelman O V 2003 Phys. Rev. E 67 041205
[13]	Tong P Q, Li B W, Hu B B 1999 Phys. Rev. B 59 8639
[14]	Rubin R J, Green W L 1971 Math. Phys. 12 1686
[15]	Lepris S, Livi R, Poiti A 1997 Phys. Rev. Lett. 78 1896
[16]	Kaburaki H, Machida M 1993 Phys. Lett. A 181 85
[17]	Hu B, Li B W, Zhao H 1998 Phys. Rev. E 57 2992
[18]	Shechtman D, Blech I, Gratias D 1984 Phys. Rev. Lett. 53 1951
[19]	Cao L S, Peng R W, Zhang R L, Zhang X F, Wang M, Huang X Q, Hu A, Jiang S S 2005 Phys. Rev. B 72 214301
[20]	Enrique M 1999 Phys. Rev. B 61 10
[21]	Huang X Q, Gong C D 1998 Phys. Rev. B 58 739
[22]	Bellisard J, Iochum B, Scoppola E, Testard D 1989 Math. Phys. 125 527
[23]	Rubin R J, Greer W L 1971 Math. Phys. 12 1686
[24]	Connor A J O, Lebowitz J L 1974 Math. Phys. 15 692
[25]	Cao Y J,Yang X 2008 Acta Phys. Sin. 57 3620 (in Chinese) [曹永军、杨旭 2008 物理学报 57 3620]

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