Ergodicity of Random-Matrix Theories: The Unitary Case

Details Ergodicity of Random-Matrix Theories: The Unitary Case Ergodicity of Random-Matrix Theories: The Unitary Case

1999-12-27

arxiv.org/abs/cond-mat/9912458v1

Phys. Rev. Lett. 84 (2000) 2833

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages

Scientific paper

10.1103/PhysRevLett.84.2833

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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