Flamm抛物面中的双组分等离子体
Two Component Plasma in a Flamm's Paraboloid
摘要：
本文研究了在耦合常数$Γ=2$的某一值下，生活在Flamm抛物面中的双组分等离子体（TCP），得到了巨正则配分函数的解析表达式。考虑了两种情况，即等离子体在具有绝缘层的半表面中和等离子体在整个表面中。明确地找到了确定$n$ -粒子截断关联函数所需的格林函数方程，在这两种情况下都证明了这一方程太复杂而不能解析求解。因此，我们提出了求解方法，将问题归结为求一个高次多项式系数的二阶线性齐次常微分方程的两个线性无关解。在平坦极限中，人们恢复了第一种情况下平面中TCP结构的解，但在第二种情况下，在视界处相反电荷的坍缩使得等离子体的结构在物理上没有很好地定义。
英文摘要：
The two component plasma (TCP) living in a Flamm's paraboloid is studied at a value of the coupling constant $Γ=2$ for which an analytic expression for the grand canonical partition function is available. Two cases are considered, the plasma in the half surface with an insulating horizon and the plasma in the whole surface. The Green's function equation necessary to determine the $n$-particle truncated correlation functions is explicitly found. In both cases this proves too complicated to be solved analytically. So we present the method of solution reducing the problem to finding the two linearly independent solutions of a linear homogeneous second order ordinary differential equation with polynomial coefficients of high degrees. In the flat limit one recovers the solution for the structure of the TCP in a plane in the first case but the collapse of opposite charges at the horizon makes the structure of the plasma physically not well defined in the second case.
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