Fermi-Pasta-Ulam β格点链系统能量载流子研究  

Energy carriers investigation in the Fermi-Pasta-Ulam β lattice

作　　者：袁宗强[1] 褚敏[1] 郑志刚[1] 

机构地区：[1]北京师范大学物理学系,北京-香港-新加坡非线性与复杂性研究联合中心,北京100875

出　　处：《物理学报》2013年第8期25-30,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11075016);中央高校基本科研业务费(批准号:201001);高等学校博士学科点专项科研基金(批准号:20100003110007)资助的课题~~

摘　　要：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.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.

关 键 词：Fermi-Pasta-Ulam格点链 声子 孤子 热传导 

分 类 号：O469[理学—凝聚态物理]