球环上的单组分等离子体和随机矩阵系综
One-component plasma on a spherical annulus and a random matrix ensemble
摘要：
已知在特殊耦合β= 2处的二维单组分等离子体，由于其自由能和所有相关性，在各种表面和各种边界条件下都是精确可解的。在这里，我们研究这个系统局限于一个球环软壁边界条件，特别注意所产生的渐近形式的二维等离子体的预期一般性质的观点。我们的研究是基于β= 2的等离子体系统的Boltzmann因子的实现，通过从球面到复平面的赤平投影，由复Gauss和Haar分布的酉矩阵构成的随机矩阵系综。
英文摘要：
The two-dimensional one-component plasma at the special coupling β= 2 is known to be exactly solvable, for its free energy and all of its correlations, on a variety of surfaces and with various boundary conditions. Here we study this system confined to a spherical annulus with soft wall boundary conditions, paying special attention to the resulting asymptotic forms from the viewpoint of expected general properties of the two-dimensional plasma. Our study is motivated by the realization of the Boltzmann factor for the plasma system with β= 2, after stereographic projection from the sphere to the complex plane, by a certain random matrix ensemble constructed out of complex Gaussian and Haar distributed unitary matrices.
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