2021/09/21 by Martin R. Zirnbauer, Zirnbauer, Martin R.
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Random Matrices and Applications #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2109.10272
openalex publication_date 2021/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The "color-flavor transformation", conceived as a kind of generalized Hubbard-Stratonovich transformation, is a variant of the Wegner-Efetov supermatrix method for disordered electron systems. Tailored to quantum systems with disorder distributed according to the Haar measure of a compact Lie group of any classical type (A, B, C, or D), it has been applied to Dyson's Circular Ensembles, random network models, disordered Floquet dynamical systems, quantum chaotic graphs, and more. We review the method and, in particular, explore its limits of validity. An application to O(N)-Haar expectations of ratios of random characteristic polynomials is given. We also sketch a novel method to treat models where the color-flavor transformation fails.