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Fermi-Pasta-Ulam (FPU) β格点链中能量输运的载流子是孤子还是声子一直存在较多的争议. 本文通过单脉冲方法, 明确了一个能量波包在该格点链系统中从声子波包转变成为孤子波包的条件, 即波包能量达到一定阈值. 基于纯四次势链的声子真空效应, 构造了由FPU-β链与纯四次势链构成的双段链系统. 通过对比研究双段链系统和单段FPU-β链中的热流, 发现低温下声子是FPU-β链中能量的主要载流子, 而随着温度的升高孤子逐步取代声子成为能量的主要载流子.
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关键词:
- Fermi-Pasta-Ulam格点链 /
- 声子 /
- 孤子 /
- 热传导
Recently, heat conduction in low-dimensional materials has attracted much attention. The energy carriers responsible for the heat conduction in the Fermi-Pasta-Ulam (FPU) β lattice is still in debate. To the best of our knowledge, the sound velocity of energy transfer has been measured to examine the properties of the energy carriers, by using both nonequilibrium and equilibrium approaches. Nevertheless, the uncertainty of the computational data is too large to distinguish between the two predictions based on soliton theory and effective-phonon theory. In this paper, the spatiotemporal propagation of a momentum excitation traveling along the FPU-β lattice is investigated. The harmonic and anharmonic couplings induce the dispersion and localization of a energy packet on the lattice, respectively. The bifurcation of a solitary wave takes place as the energy of the packet exceeds a threshold. Based on the "acoustic vacuum" phenomenon in the pure quartic lattice, a two-segment lattice composed of the FPU-β chain and the pure quartic chain is constructed. The heat flux in the two-segment lattice is studied to compare with that in the FPU-β lattice. The ratio of the heat flux of the two-segment lattice to the FPU-β lattice increases monotonically as temperature rises. We conclude that phonons are the majority energy carriers in the low temperature regime, while solitons become dominant carriers as the temperature increases. The spatiotemporal propagation of a momentum excitation traveling along the two-segment lattice is also investigated. Phonon packets excited in the FPU-β part are reflected at the interface while solitary waves can pass through the interface. This supports microscopically our conclusion on the energy carriers in the FPU-β lattice.-
Keywords:
- Fermi-Pasta-Ulam lattice /
- phonon /
- soliton /
- heat conduction
[1] Lepri S, Livi R, Politi A 1997 Phys. Rev. Lett. 78 1896
[2] Chang C W, Okawa D, Garcia A, Majumdar A, Zettl A 2008 Phys. Rev. Lett. 101 075903
[3] Nika D L, Ghosh S, Pokailov E P, Balandin A A 2009 Appl. Phys. Lett. 94 203103
[4] Casati G, Ford J, Vivaldi F, Visscher W M 1984 Phys. Rev. Lett. 52 1861
[5] Prosen T, Robnick M 1992 J. Phys. A 25 3449
[6] Hu B, Li B, Zhao H 1998 Phys. Rev. E 57 2992
[7] Li B, Zhao H, Hu B 2001 Phys. Rev. Lett. 86 63
[8] Dhar A, Lebowitz J L 2008 Phys. Rev. Lett. 100 134301
[9] Saito K, Dhar A 2010 Phys. Rev. Lett. 104 040601
[10] Wang L, He D, Hu B 2010 Phys. Rev. Lett. 105 160601
[11] Lepri S, Livi R, Politi A 2003 Phys. Rep. 377 1
[12] Dhar A 2008 Adv. Phys. 57 457
[13] Li N, Ren J, Wang L, Zhang G, Hänggi P, Li B 2012 Rev. Mod. Phys. 84 1045
[14] Fermi E, Pasta J, Ulam S 1955 Los Alamos Document No. LA-1940
[15] Zhang F, Isbister D J, Evans D J 2000 Phys. Rev. E 61 3541
[16] Zhang F, Isbister D J, Evans D J 2001 Phys. Rev. E 64 021102
[17] Aoki K, Kusnezov D 2001 Phys. Rev. Lett. 86 4029
[18] Zhao H 2006 Phys. Rev. Lett. 96 140602
[19] Li N, Tong P, Li B 2006 Europhys. Lett. 75 49
[20] Li N, Li B, Flach S 2010 Phys. Rev. Lett. 105 054102
[21] Mahan G D 2006 Phys. Rev. B 74 094304
[22] Neogi S, Mahan G D 2008 Phys. Rev. B 78 064306
[23] Sen S, Mohan T R K 2009 Phys. Rev. E 79 036603
[24] ávalos E, Sun D, Doney R L, Sen S 2011 Phys. Rev. E 84 046610
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[1] Lepri S, Livi R, Politi A 1997 Phys. Rev. Lett. 78 1896
[2] Chang C W, Okawa D, Garcia A, Majumdar A, Zettl A 2008 Phys. Rev. Lett. 101 075903
[3] Nika D L, Ghosh S, Pokailov E P, Balandin A A 2009 Appl. Phys. Lett. 94 203103
[4] Casati G, Ford J, Vivaldi F, Visscher W M 1984 Phys. Rev. Lett. 52 1861
[5] Prosen T, Robnick M 1992 J. Phys. A 25 3449
[6] Hu B, Li B, Zhao H 1998 Phys. Rev. E 57 2992
[7] Li B, Zhao H, Hu B 2001 Phys. Rev. Lett. 86 63
[8] Dhar A, Lebowitz J L 2008 Phys. Rev. Lett. 100 134301
[9] Saito K, Dhar A 2010 Phys. Rev. Lett. 104 040601
[10] Wang L, He D, Hu B 2010 Phys. Rev. Lett. 105 160601
[11] Lepri S, Livi R, Politi A 2003 Phys. Rep. 377 1
[12] Dhar A 2008 Adv. Phys. 57 457
[13] Li N, Ren J, Wang L, Zhang G, Hänggi P, Li B 2012 Rev. Mod. Phys. 84 1045
[14] Fermi E, Pasta J, Ulam S 1955 Los Alamos Document No. LA-1940
[15] Zhang F, Isbister D J, Evans D J 2000 Phys. Rev. E 61 3541
[16] Zhang F, Isbister D J, Evans D J 2001 Phys. Rev. E 64 021102
[17] Aoki K, Kusnezov D 2001 Phys. Rev. Lett. 86 4029
[18] Zhao H 2006 Phys. Rev. Lett. 96 140602
[19] Li N, Tong P, Li B 2006 Europhys. Lett. 75 49
[20] Li N, Li B, Flach S 2010 Phys. Rev. Lett. 105 054102
[21] Mahan G D 2006 Phys. Rev. B 74 094304
[22] Neogi S, Mahan G D 2008 Phys. Rev. B 78 064306
[23] Sen S, Mohan T R K 2009 Phys. Rev. E 79 036603
[24] ávalos E, Sun D, Doney R L, Sen S 2011 Phys. Rev. E 84 046610
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