Stilllinger-Lovett和规则的推广 二维果冻

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摘要翻译：
在经典库仑流体的平衡统计力学中，库仑势的长程尾导致电荷关联函数的Stillinger-Lovett和规则。对于浸没在中和背景中的电荷$q$-移动粒子的果冻模型，固定一个$q$-电荷会产生电荷密度的屏蔽云，其零阶矩和二阶矩仅由Stillinger-Lovett和规则决定。本文在客电荷$Z>-2/γ$的热力学稳定性范围内，将这些和规则推广到二维果冻内部的点状客电荷$Zq$周围诱导的屏蔽云，耦合常数为$\gamma=\betaq^2$($\beta$为逆温度）。推导的基础是二维水母在耦合$\γ$=（偶数正整数）到离散的一维反交换场理论的映射技术；我们假设最终的结果对于流体状态对应的所有实际值$\gamma$仍然有效。对于任意耦合，广义和则再现了标准Z=1和平凡Z=0的结果。在Debye-H\\\Uckel极限$\\γ\\0和自由费米子点$\\γ=2$处也进行了检验。广义二阶矩和规则提供了空间中诱导电荷密度可能的符号振荡的一些精确信息。
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英文标题：
《A Generalization of the Stillinger-Lovett Sum Rules for the
  Two-Dimensional Jellium》
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作者：
L. Samaj
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  In the equilibrium statistical mechanics of classical Coulomb fluids, the long-range tail of the Coulomb potential gives rise to the Stillinger-Lovett sum rules for the charge correlation functions. For the jellium model of mobile particles of charge $q$ immersed in a neutralizing background, the fixing of one of the $q$-charges induces a screening cloud of the charge density whose zeroth and second moments are determined just by the Stillinger-Lovett sum rules. In this paper, we generalize these sum rules to the screening cloud induced around a pointlike guest charge $Z q$ immersed in the bulk interior of the 2D jellium with the coupling constant $\Gamma=\beta q^2$ ($\beta$ is the inverse temperature), in the whole region of the thermodynamic stability of the guest charge $Z>-2/\Gamma$. The derivation is based on a mapping technique of the 2D jellium at the coupling $\Gamma$ = (even positive integer) onto a discrete 1D anticommuting-field theory; we assume that the final results remain valid for all real values of $\Gamma$ corresponding to the fluid regime. The generalized sum rules reproduce for arbitrary coupling $\Gamma$ the standard Z=1 and the trivial Z=0 results. They are also checked in the Debye-H\"uckel limit $\Gamma\to 0$ and at the free-fermion point $\Gamma=2$. The generalized second-moment sum rule provides some exact information about possible sign oscillations of the induced charge density in space.
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PDF链接：
https://arxiv.org/pdf/705.1416

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关键词：Still Love ING Ill GER 广义 规则 电荷 屏蔽 immersed