具有横向和纵向振动的链中的反常输运和声子重整化
Anomalous transport and phonon renormalization in a chain with transverse and longitudinal vibrations
摘要：
本文研究了耦合原子链中的热输运问题，耦合原子链可以在纵向和横向振动。粒子通过高达立方阶的非谐势相互作用。这个问题用量子力学来处理。我们首先计算的声子频率自洽考虑到非谐相互作用。我们发现，对于所有的模式，频率必须有线性色散与波矢量$q$小$q$，而不管他们的裸色散。然后，我们计算声子弛豫率$Γ_i(q)$，其中$i$是偏振指数的模式，在一个自洽近似的基础上的二阶微扰图。我们发现纵声子的弛豫速率为$Γ_x(q) \propto q^{3/2}$，横声子的弛豫速率为$Γ_y(q) \propto q^2$ .这些结果对$N$颗粒链的热导率$κ(N)$的结果是$κ(N) \propto N^{1/2}$。
英文摘要：
We study thermal transport in a chain of coupled atoms, which can vibrate in longitudinal as well as transverse directions. The particles interact through anharmonic potentials upto cubic order. The problem is treated quantum mechanically. We first calculate the phonon frequencies self-consistently taking into account the anharmonic interactions. We show that for all the modes, frequencies must have linear dispersion with wave-vector $q$ for small $q$ irrespective of their bare dispersions. We then calculate the phonon relaxation rates $Γ_i(q)$, where $i$ is the polarization index of the mode, in a self-consistent approximation based on second order perturbation diagrams. We find that the relaxation rate for the longitudinal phonon, $Γ_x(q) \propto q^{3/2}$, while that for the transverse phonon $Γ_y(q) \propto q^2$. The consequence of these results on the thermal conductivity $κ(N)$ of a chain of $N$ particles is that $κ(N) \propto N^{1/2}$.
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