半空间中量子二维的关联与求和规则 单组分等离子体

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摘要翻译：
本文是前文[L.{v{S}}amaj和B.Jancovici,2007{it J.stat.mech.}P02002]的继续；对于平面硬壁（无像力）约束的半空间中的近似经典量子流体，我们推广了平衡点统计量的Wigner-Kirkwood展开式。作为一个更详细研究的模型系统，我们考虑量子二维单组分等离子体：一种带电粒子通过二维对数库仑势相互作用，在相反符号的均匀带电背景中，使总电荷消失。对应的经典系统在各种几何条件下都是精确可解的，包括现在的半平面，当$βe2=2$时，其中$β$是逆温度，$e$是粒子的电荷：所有的经典$n$-体密度都是已知的。对于量子单组分等离子体，通过启发式宏观论证，很久以前就已经导出了两个关于截断二体密度（其中一个是密度分布）的求和规则：一个是关于截断二体密度沿壁的渐近形式的求和规则，另一个是关于结构因子的偶极矩的求和规则。在$\betae^2=2$的二维情形下，我们现在有了这两个量子密度的$\hbar^2$级的显式表达式，因此我们可以在微观上检查这个级的和规则。检查是积极的，加强了求和规则是正确的想法。
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英文标题：
《Correlations and sum rules in a half-space for a quantum two-dimensional
  one-component plasma》
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作者：
B. Jancovici, 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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一级分类：Physics        物理学
二级分类：Quantum Physics        量子物理学
分类描述：Description coming soon
描述即将到来
--

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英文摘要：
  This paper is the continuation of a previous one [L. {\v{S}}amaj and B. Jancovici, 2007 {\it J. Stat. Mech.} P02002]; for a nearly classical quantum fluid in a half-space bounded by a plain plane hard wall (no image forces), we had generalized the Wigner-Kirkwood expansion of the equilibrium statistical quantities in powers of Planck's constant $\hbar$. As a model system for a more detailed study, we consider the quantum two-dimensional one-component plasma: a system of charged particles of one species, interacting through the logarithmic Coulomb potential in two dimensions, in a uniformly charged background of opposite sign, such that the total charge vanishes. The corresponding classical system is exactly solvable in a variety of geometries, including the present one of a half-plane, when $\beta e^2=2$, where $\beta$ is the inverse temperature and $e$ is the charge of a particle: all the classical $n$-body densities are known. For the quantum one-component plasma, two sum rules involving the truncated two-body density (and, for one of them, the density profile) have been derived, a long time ago, by heuristic macroscopic arguments: one sum rule is about the asymptotic form along the wall of the truncated two-body density, the other one is about the dipole moment of the structure factor. In the two-dimensional case at $\beta e^2=2$, we have now explicit expressions up to order $\hbar^2$ of these two quantum densities, thus we can microscopically check the sum rules at this order. The checks are positive, reinforcing the idea that the sum rules are correct.
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PDF链接：
https://arxiv.org/pdf/704.2316

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关键词：等离子体 等离子 correlations Continuation Dimensional quantum 截断 硬壁 库仑 规则