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One-component plasma on a spherical annulus and a random matrix ensemble

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.