构建无倒易散射过程的立方非线性晶格
Construction of cubic nonlinear lattice free from umklapp processes
AI总结：
提出包含立方长程非线性的无倒易散射晶格（UFL），推导非线性耦合常数解析式，数值模拟证实其抑制倒易散射过程，热导率更接近弹道输运。
摘要：
我们提出了一种新型无倒易散射晶格（UFL），其中倒易散射过程完全不存在。所提出的UFL包含立方长程非线性，这是以往研究未涉及的特征。本文通过施加数学条件，推导出立方非线性耦合常数的解析表达式，使得粒子对之间的非线性耦合强度随其分离距离成反比衰减。通过与Fermi-Pasta-Ulam-Tsingou（FPUT）晶格的数值比较，证实了所提出晶格中不存在倒易散射过程。此外，通过分子动力学模拟研究了所提出晶格在非平衡稳态下的热导率。与原始FPUT晶格相比，所提出的UFL更接近弹道输运。结果表明，立方非线性引起的倒易散射过程在所提出的UFL中受到抑制。此外，与仅含四次非线性的UFL相比，长程相互作用的截断在所提出的晶格中起重要作用。
英文摘要：
We propose a novel type of umklapp-free lattice (UFL), where umklapp processes are completely absent. The proposed UFL incorporates cubic long-range nonlinearity, a feature not addressed in previous studies. In this paper, we derive an analytical expression for the cubic nonlinear coupling constants by imposing mathematical conditions such that the nonlinear coupling strength between particle pairs decays inversely with their separation distance. The absence of umklapp processes in the proposed lattice is confirmed through numerical comparisons with the Fermi-Pasta-Ulam-Tsingou (FPUT) lattice. Furthermore, molecular dynamics simulations are performed to investigate the thermal conductivity of the proposed lattice in the non-equilibrium steady state. Compared to the original FPUT lattice, the proposed UFL is closer to ballistic transport. Our results demonstrate that the umklapp processes induced by cubic nonlinearity are suppressed in the proposed UFL. Moreover, compared to the UFL with only quartic nonlinearity, truncation of long-range interactions plays a significant role in the proposed lattice.
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