论文标题
ISO- $ G_2 $流程通过有效的配对互动的可实现性
Realizability of Iso-$g_2$ Processes via Effective Pair Interactions
论文作者
论文摘要
统计力学中的一个杰出问题是确定对配对相关功能的规定功能形式$ g_2（r）$ [或等效地，在某种数字密度$ρ$的结构因子因子$ s（k）$]可以通过$ d $ d $ d $ d $ d $ d $ d $ d $ d $ d.d $ d.d $ d.d $ d $ d。张 - 托夸尔夸尔猜想指出，无论是从非平衡还是平衡系统中，任何可实现的成对统计量都可以通过涉及多达两体相互作用的平衡系统来实现。 鉴于这种猜想，我们研究了非平衡ISO- $ g_2 $过程的可变性问题，即确定密度依赖性有效电位，产生平衡状态，其中$ g_2 $在积极范围内保持不变。 使用一种确定有效潜力的精确反向方法，该方法与所有$ r $ $ g_2（r）$的假设功能形式匹配，所有$ r $和$ s（k）$对于所有$ k $，我们表明单位step函数$ g_2 $，这是硬态潜力的零密度限制，即硬化的零密度限制，在包装上是$ pake $ d的，即$ pak $ d $ d = 0.49 $ d = 49 $ d = 0.49 $ d = 49 $ d = 49。对于$ d = 2 $和3，它可以实现至最大``terminal''包装分数$ ϕ_c = 1/2^d $，在该系统中，系统是非常一体式的，这意味着明确已知的实现必要条件以实现通过$ ϕ_C $。 对于$ ϕ $接近但低于$ ϕ_c $，有效潜力的大$ r $行为完全由功能表格$ \ exp [-κ（ϕ）r] $ for $ d = 1 $，$ d = 1 $，$ r^{ - 1/2} \ exp [-texp [-tect [-x（ϕ）$ for $ d = 2 $ d = 2 $，和$ r^$ r^$ r^{-1]表格）对于$ d = 3 $，其中$κ^{ - 1}（ϕ）$是筛选长度，对于$ ϕ = ϕ_c $，大$ r $的电势由纯库仑形式在相应的维度中，如torquato和torquato和stillinger [\ textit {phys phys physs所预测的。 Rev.E}，68，041113 1-25（2003）]。
An outstanding problem in statistical mechanics is the determination of whether prescribed functional forms of the pair correlation function $g_2(r)$ [or equivalently, structure factor $S(k)$] at some number density $ρ$ can be achieved by $d$-dimensional many-body systems. The Zhang-Torquato conjecture states that any realizable set of pair statistics, whether from a nonequilibrium or equilibrium system, can be achieved by equilibrium systems involving up to two-body interactions. In light of this conjecture, we study the realizability problem of the nonequilibrium iso-$g_2$ process, i.e., the determination of density-dependent effective potentials that yield equilibrium states in which $g_2$ remains invariant for a positive range of densities. Using a precise inverse methodology that determines effective potentials that match hypothesized functional forms of $g_2(r)$ for all $r$ and $S(k)$ for all $k$, we show that the unit-step function $g_2$, which is the zero-density limit of the hard-sphere potential, is remarkably numerically realizable up to the packing fraction $ϕ=0.49$ for $d=1$. For $d=2$ and 3, it is realizable up to the maximum ``terminal'' packing fraction $ϕ_c=1/2^d$, at which the systems are hyperuniform, implying that the explicitly known necessary conditions for realizability are sufficient up through $ϕ_c$. For $ϕ$ near but below $ϕ_c$, the large-$r$ behaviors of the effective potentials are given exactly by the functional forms $\exp[-κ(ϕ) r]$ for $d=1$, $r^{-1/2}\exp[-κ(ϕ) r]$ for $d=2$, and $r^{-1}\exp[-κ(ϕ) r]$ (Yukawa form) for $d=3$, where $κ^{-1}(ϕ)$ is a screening length, and for $ϕ=ϕ_c$, the potentials at large $r$ are given by the pure Coulomb forms in the respective dimensions, as predicted by Torquato and Stillinger [\textit{Phys. Rev. E}, 68, 041113 1-25 (2003)].
