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Ergodicity of Random-Matrix Theories: The Unitary Case

Z. Pluhar·H. A. Weidenmueller
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Abstract

We prove ergodicity of unitary random-matrix theories by showing that the autocorrelation function with respect to energy or magnetic field strength of any observable vanishes asymptotically. We do so using Efetov's supersymmetry method, a polar decomposition of the saddle-point manifold, and an asymptotic evaluation of the boundary terms generated in this fashion.

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Z. Pluhar, H. A. Weidenmueller. 1999-12-27. Ergodicity of Random-Matrix Theories: The Unitary Case. https://doi.org/10.1103/physrevlett.84.2833

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