1996/09/14 by Martin R. Zirnbauer, Martin R Zirnbauer · 3 citations
Chemistry · Physics and Astronomy · #Molecular spectroscopy and chirality #Quantum Chromodynamics and Particle Interactions #Quantum chaos and dynamical systems #chao-dyn #cond-mat #nlin.CD
paper · pdf · doi:10.1088/0305-4470/29/22/013
published as J. Phys. A 29 (1996) 7113 · 19 pages, REVTEX, to appear in J. Phys. A (Math. and Gen.)
arxiv created 1996/09/14 · openalex publication_date 1996/11/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
A generalized Hubbard-Stratonovitch transformation relating an integral over random unitary N times N matrices to an integral over Efetov's unitary sigma model manifold, is introduced. This transformation adapts the supersymmetry method to disordered and chaotic systems that are modeled not by a Hamiltonian but by their scattering matrix or time-evolution operator. In contrast to the standard method, no saddle-point approximation is made, and no massive modes have to be eliminated. This first paper on the subject applies the generalized Hubbard-Stratonovitch transformation to Dyson's Circular Unitary Ensemble. It is shown how to use a supersymmetric variant of the Harish-Chandra-Itzykson-Zuber formula to compute, in the large-N limit, the n-level correlation function for any n. Nontrivial applications to random network models, quantum chaotic maps, and lattice gauge theory, are expected.