Generalized self-consistent reservoir model for normal and anomalous heat transport in quantum harmonic chains
Generalized self-consistent reservoir model for normal and anomalous heat transport in quantum harmonic chains
复制标题
量子谐波链中正常和反常热传输的广义自洽储层模型
DOI：
10.1103/physreve.99.062104
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Kiminori Hattori and Miyuki Yoshikawa
中科院分区：
文献类型：
--
作者：
Hattori Kiminori;Sambonchiku Masaya;Kiminori Hattori and Miyuki Yoshikawa
虚拟随机储层将散射和失相机制结合到与这些储层接触的系统中。非平衡态绿色函数形式或量子朗之万方程形式描述的相关的自能的耦合。在这项研究中，我们研究了热输运在一个无限扩展的量子谐波链的有限段具有相等的自能量在每个网站上使用自洽水库的方法。在这种设置中，整个系统是晶格平移不变的，因此不匹配的边界被排除在模型之外。在自洽绝热条件下求解Landauer-Büttiker方程，定量地阐明了热诱导的弹道输运到扩散输运的交叉及其与温度相关的平均自由程的标度关系，并指出对于线性自能，正常输运出现在扩散极限，而非线性高阶输运一般导致反常输运.这些意见的物理意义进行了讨论，在一个无质量的戈德斯通模式的持久性以及总的线性动量守恒。
Fictitious stochastic reservoirs incorporate scattering and dephasing mechanisms into the system in contact with these reservoirs. The reservoir-system coupling is described by the related self-energy in terms of the nonequilibrium Green's function formalism or equivalently the quantum Langevin equation formalism. In this study, we investigate thermal transport in a finite segment of an infinitely extended quantum harmonic chain with an equal self-energy at each site by using the self-consistent reservoir approach. In this setup, the entire system is lattice translation invariant so that mismatched boundaries are excluded from the model. Solving the Landauer-Büttiker equations under the self-consistent adiabatic condition, we quantitatively elucidate a thermally induced crossover of ballistic-to-diffusive transport and its scaling relation prescribed by a temperature-dependent mean free path. It is also shown that normal transport emerges in the diffusive limit for a linear self-energy, while nonlinear higher-order ones generically lead to anomalous transport. Physical implications of these observations are discussed in terms of the persistence of a massless Goldstone mode as well as the conservation of total linear momentum.