Classical and quantum continuum percolation with hard core interactions
Classical and quantum continuum percolation with hard core interactions
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具有硬核相互作用的经典和量子连续渗透
DOI：
10.1063/1.460401
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发表时间：
1991
影响因子：
4.4
通讯作者：
J. Wright
中科院分区：
文献类型：
--
作者：
J. Saven;J. Skinner;J. Wright
我们研究了三维连续介质中球体的经典和量子渗流。每个球都有一个直径为σ的不可穿透的核心，如果两个球的中心之间的距离小于d，则认为它们是直连的。我们计算了临界渗流密度作为σ/d的函数。在经典问题中，这是一个无限连通球簇首先形成的密度ρc。在量子问题中，我们研究了一个紧束缚模型，其中两个球之间的跳跃矩阵元只有当它们直接相连时才是非零的。在这种情况下，临界密度ρq是哈密顿量的本征态首次扩展的密度。我们的方法使用了蒙特卡罗模拟和有限尺寸标度技术，对于量子问题，使用了量子连通性的概念。我们发现，ρ_c和ρ_q都表现出作为σ/d的函数的非单调行为。我们还发现，对于所有σ/d的值，ρ_q和ρ_c，尽管阈值之比d<...
We study the classical and quantum percolation of spheres in a three‐dimensional continuum. Each sphere has an impenetrable hard core of diameter σ, and two spheres are considered to be directly connected if the distance between their centers is less than d. We calculate the critical percolation density as a function of σ/d. In the classical problem this is the density ρc at which an infinite cluster of connected spheres first forms. In the quantum problem, we study a tight‐binding model where the hopping matrix element between two spheres is nonzero only if they are directly connected. In this case the critical density ρq is the density at which the eigenstates of the Hamiltonian first become extended. Our method uses Monte Carlo simulation and finite‐size scaling techniques, and for the quantum problem, the concept of quantum connectivity. We find that both ρc and ρq exhibit nonmonotonic behavior as a function of σ/d. We also find that for all values of σ/d, ρq>ρc, although the ratio of the thresholds d...