当前位置: X-MOL 学术Ann. Phys. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Normal modes for N identical particles: A study of the evolution of collective behavior from few-body to many-body
Annals of Physics ( IF 3 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.aop.2020.168219
D.K. Watson

Normal mode dynamics are ubiquitous underlying the motions of diverse systems from rotating stars to crystal structures. These behaviors are composed of simple collective motions of particles which move with the same frequency and phase, thus encapsulating many-body effects into simple dynamic motions. In regimes such as the unitary regime for ultracold Fermi gases, a single collective mode can dominate, leading to simple behavior as seen in superfluidity. I investigate the evolution of collective motion as a function of N for five types of normal modes obtained from an L=0 group theoretic solution of a general Hamiltonian for confined, identical particles. I show using simple analytic forms that the collective behavior of few-body systems, with the well known motions of molecular equivalents such as ammonia and methane, evolves smoothly to the collective motions expected for large N ensembles. The transition occurs at quite low values of N. I study a Hamiltonian known to support collective behavior, the Hamiltonian for Fermi gases in the unitary regime. I analyze the evolution of both frequencies and the coefficients that mix the radial and angular coordinates which both depend on interparticle interactions. This analysis reveals two phenomena that could contribute to the viability of collective behavior. First the mixing coefficients go to zero or unity, i.e. no mixing, as N becomes large resulting in solutions that do not depend on the details of the interparticle potential as expected for this unitary regime, and that manifest the symmetry of an underlying approximate Hamiltonian. Second, the five normal mode frequencies which are all close for low values of N, separate as N increases, creating large gaps that can, in principle, offer stability to collective behavior if mechanisms to prevent the transfer of energy to other modes exist (such as low temperature) or can be constructed.

中文翻译:

N个相同粒子的正常模式:集体行为从少体到多体演化的研究

在从旋转恒星到晶体结构的各种系统的运动中,常模动力学无处不在。这些行为由以相同频率和相位移动的粒子的简单集体运动组成,从而将多体效应封装为简单的动态运动。在诸如超冷费米气体的单一机制之类的机制中,单一的集体模式可以占主导地位,导致在超流中看到的简单行为。我研究了五种类型的正常模式的集体运动的演变作为 N 的函数,这些正常模式是从有限的相同粒子的一般哈密顿量的 L=0 群理论解中获得的。我使用简单的分析形式展示了少体系统的集体行为,以及众所周知的分子等价物(如氨和甲烷)的运动,平滑地演变为大型 N 系综所期望的集体运动。转变发生在相当低的 N 值下。我研究了一个已知支持集体行为的哈密顿量,即统一制度中费米气体的哈密顿量。我分析了两个频率的演变以及混合径向和角坐标的系数,这两者都取决于粒子间的相互作用。这一分析揭示了两种可能有助于集体行为可行性的现象。首先,混合系数变为零或统一,即没有混合,因为 N 变大导致解不依赖于该单一制度所预期的粒子间势能的细节,并且表现出潜在的近似哈密顿量的对称性。第二,
更新日期:2020-08-01
down
wechat
bug