Ergodicity of Unitary Random-Matrix Ensembles

✍ Scribed by Z. Pluhař; H.A. Weidenmüller

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 191 KB
• Volume: 282
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.2000.6029

✦ Synopsis

Using Efetov's supersymmetry method, we prove the ergodicity of a wide class of unitary random-matrix ensembles. We do so by showing that the connected part of the autocorrelation function of any observable vanishes asymptotically. The essential elements of the proof consist in a polar decomposition of the saddle-point manifold, in the construction of the Efetov Wegner terms generated in this way, and in an asymptotic expansion of these terms in inverse powers of the relevant parameter.