The U(1) problem in chiral random matrix models

We show that conventional asymmetric chiral random matrix models (ChRMM), with a gaussian distribution in the asymmetry, provide for a screening of the topological charge and a resolution of the U(1) problem in the unquenched approximation. Our exact results to order 1/N are in agreement with numerical estimates using large ensembles of asymmetric ChRMM with gaussian distributions. (orig.)30 refs.Available from TIB Hannover: RO 801(97-10) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

New developments in non-hermitian random matrix models

In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) a diagrammatic approach based on a 1/N expansion (b) a generalization of the addition theorem (R-transformation) (c) a conformal transformation on the position of pertinent singularities (d) a 'phase' analysis using appropriate partition functions (e) a number of two-point functions and the issue of universality. (orig.)Available from FIZ Karlsruhe / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Various shades of Blue's functions

We discuss random matrix models in terms of elementary operations on Blue's functions (functional inverse of Green's functions). We show that such operations embody the essence of a number of physical phenomena whether at/or away from the critical points. We illustrate these assertions by borrowing on a number of recent results in effective QCD in vacuum and matter. We provide simple physical arguments in favor of the universality of the continuum QCD spectral oscillations, whether at zero virtuality, in the bulk of the spectrum or at the chiral critical points. We also discuss effective quantum systems of disorder with strong or weak dissipation (Hatano-Nelson localization). (orig.)Presented at the 37. Cracow School of Theoretical Physics, Zakopane (Poland), 1997Available from TIB Hannover: RO 801(97-63) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman