2014/10/31 by Yan V. Fyodorov, Y. V. Fyodorov, André Nock +1
Mathematics · Physics and Astronomy · #Chaotic #Circular ensemble #Gaussian #Matrix (chemical analysis) #Orthogonal polynomials #Quantum chaos #Quantum chaos and dynamical systems #Random Matrices and Applications #Random matrix #Randomness #Resolvent #Spectral Theory in Mathematical Physics #cond-mat.dis-nn #cond-mat.mes-hall #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1007/s10955-015-1209-x
published as Journal of Statistical Physics, Volume 159, Issue 4, Pages 731-751, Year 2015 · 25 pages (2 figures); published version (conclusion added, minor changes)
openalex publication_date 2015/02/18 · arxiv created 2015/04/22 · arxiv updated 2015/04/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 Kab 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.