非简谐振子链的热化及其与动力学理论的比较
Thermalization of oscillator chains with onsite anharmonicity and comparison with kinetic theory
摘要：
我们进行微观分子动力学模拟的粒子链与现场的非谐性研究松弛的空间均匀状态的平衡，并直接比较模拟与相应的玻尔兹曼-佩尔斯动力学理论。维格纳函数作为微观水平和动力学水平之间的公共界面。我们证明了初始瞬态时间间隔后的定量协议。特别是，除了能量守恒，我们观察到额外的准守恒的声子密度，通过相关的微观场变量的系综平均定义和精确保存的动力学方程。在超动力学时间尺度上，密度准守恒丢失，而能量保持守恒，我们找到了密度最终弛豫到其正则系综值的证据。然而，精确的机制仍然是未知的，并且没有被玻尔兹曼-佩尔斯方程捕获。
英文摘要：
We perform microscopic molecular dynamics simulations of particle chains with an onsite anharmonicity to study relaxation of spatially homogeneous states to equilibrium, and directly compare the simulations with the corresponding Boltzmann-Peierls kinetic theory. The Wigner function serves as common interface between the microscopic and kinetic level. We demonstrate quantitative agreement after an initial transient time interval. In particular, besides energy conservation, we observe the additional quasi-conservation of the phonon density, defined via an ensemble average of the related microscopic field variables and exactly conserved by the kinetic equations. On super-kinetic time scales, density quasi-conservation is lost while energy remains conserved, and we find evidence for eventual relaxation of the density to its canonical ensemble value. However, the precise mechanism remains unknown and is not captured by the Boltzmann-Peierls equations.
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