On Random Matrix Averages Involving Half-Integer Powers of GOE Characteristic Polynomials

Abstract

Correlation functions involving products and ratios of half-integer powers of characteristic polynomials of random matrices from the Gaussian Orthogonal Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT) to physics of quantum chaotic systems, and beyond. We provide an explicit evaluation of the large-$N$ limits of a few non-trivial objects of that sort within a variant of the supersymmetry formalism, and via a related but different method. As one of the applications we derive the distribution of an off-diagonal entry $K_{ab}$ of the resolvent (or Wigner $K$-matrix) of GOE matrices which, among other things, is of relevance for experiments on chaotic wave scattering in electromagnetic resonators.

25 pages (2 figures); published version (conclusion added, minor changes)

References in corpus (4)

• Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
• Universal statistics of the local Green's function in quantum chaotic systems with absorption
• Completing the picture for the smallest eigenvalue of real Wishart matrices
• On Universality for Orthogonal Ensembles of Random Matrices

Cited by in corpus (4)

• Random matrix theory of quantum transport in chaotic cavities with non-ideal leads
• Resonance width distribution in RMT: Weak coupling regime beyond Porter-Thomas
• Distribution of Off-Diagonal Cross Sections in Quantum Chaotic Scattering: Exact Results and Data Comparison
• Quantum chaos and level dynamics