Correlations and symmetry breaking in gapped matrix models

摘要

Some puzzles which arise in matrix models with multiple cuts are presented. They are present in the smoothed eigenvalue correlators of these models. First a method is described to calculate smoothed eigenvalue correlators in random matrix models with eigenvalues distributed in a single cut. Previous known results are reproduced. The method is extended to symmetric two-cut random matrix models. The correlators are written in a form suitable for application to mesoscopic systems. Connections are made with the smooth correlators derived using the orthogonal polynomial method. A few interesting observations are made regarding even and odd density-density;correlators and crossover correlators in Z(2) symmetric random matrix models. A symmetry breaking parameter C is identified in the smooth correlators for all beta=1, 2, and 4. [References: 11]