利用设计者外势研究布朗粒子的超均匀密度分布
Hyperuniform Density Distributions of Brownian Particles via Designer External Potentials
摘要：
无序超均匀性（Disordered hyperuniformity，DHU）是近年来发现的一种新的多体系统状态，其特征是具有类似于理想晶体的无规化无限波长密度涨落，但又具有类似于液体或玻璃的无定形结构。在这里，我们研究布朗粒子的平衡DHU状态的外部势诱导。特别是，我们解析推导出充分条件的外部潜力，以实现不同类的DHU密度分布的布朗粒子在热平衡，基于相应的Smoluchowski方程的定态解。我们表明，对于一个广泛的紧束缚势，所需的DHU状态的布朗粒子可以控制和实现施加适当的超均匀性条件的潜力。此外，我们发现，在这些系统中的热运动往往会增强超均匀性。我们还分析了初始密度分布（超均匀或非超均匀）的演化动力学所需的平衡DHU状态所确定的规定的外部潜力，这是耦合与施加的潜力相关联的力场的全谱。我们发现，虽然瞬态密度分布可以迅速发展的本地模式，让人想起那些在平衡分布，这是由外部电位引起的快速动态，整体分布仍然是由初始密度波动，通过缓慢的扩散动力学放松调制。我们的研究对设计师DHU材料的制造有影响。
英文摘要：
Disordered hyperuniformity (DHU) is a recently discovered novel state of many-body systems that is characterized by vanishing normalized infinite-wavelength density fluctuations similar to a perfect crystal, yet possesses an amorphous structure like a liquid or glass. Here we investigate equilibrium DHU states of Brownian particles induced by external potentials. In particular, we analytically derive sufficient conditions on the external potentials in order to achieve distinct classes of DHU density distributions of Brownian particles in thermal equilibrium, based on the stationary-state solutions of the corresponding Smoluchowski equation. We show for a wide spectrum of tight-binding potentials, the desirable DHU states of Brownian particles can be controlled and achieved by imposing proper hyperuniformity conditions on the potentials. Moreover, we find that thermal motions in these systems tend to enhance hyperuniformity. We also analyze the evolution dynamics of an initial density distribution (hyperuniform or non-hyperuniform) to the desirable equilibrium DHU state determined by the prescribed external potentials, which is shown to be coupled with the full spectra of the force fields associated with the imposed potentials. We find that although the transient density distribution can rapidly develop local patterns reminiscent of those in the equilibrium distribution, which is governed by the fast dynamics induced by the external potential, the overall distribution is still modulated by the initial density fluctuations which are relaxed through slow diffusive dynamics. Our study has implications for the fabrication of designer DHU materials.
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