Eltohfa M, Wang Xinghan, Griffin Colton M, Robicheaux F
Department of Physics and Astronomy, <a href="https://ror.org/02dqehb95">Purdue University, West Lafayette</a>, Indiana 47906, USA.
Phys Rev E. 2024 Jul;110(1-1):014114. doi: 10.1103/PhysRevE.110.014114.
One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of pointlike particles, typically the dominant process for reaching thermal equilibrium in higher-dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential V_{ij}∝1/|x_{i}-x_{j}|^{n} or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equation to evolve a perturbed thermal state with temperature T toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low-density limit. For the inverse power-law potential, the rate of thermalization is proportional to ρ^{2}T^{1/2-1/n}, where ρ is the number density. The corresponding proportionality constant decreases with increasing n.
一维系统，如纳米线或沿强磁场线移动的电子，具有独特的热化物理过程。点状粒子的二元碰撞，通常是高维系统达到热平衡的主导过程，却无法使一维系统热化。我们研究稀薄经典一维气体如何通过三体碰撞实现热化。我们考虑一个由相同经典点状粒子组成的系统，其粒子间具有成对排斥的逆幂律势(V_{ij}∝1/|x_{i}-x_{j}|^{n})或成对的 Lennard-Jones 势。使用蒙特卡罗方法，我们计算一个碰撞核，并将其用于玻尔兹曼方程，以使温度为(T)的微扰热态向平衡态演化。我们解释了碰撞核的形状及其对系统参数的依赖性。此外，我们对多体气体进行了分子动力学模拟，并在低密度极限下显示出与玻尔兹曼演化的一致性。对于逆幂律势，热化速率与(\rho^{2}T^{1/2 - 1/n})成正比，其中(\rho)是数密度。相应的比例常数随(n)的增加而减小。
