Smoothed Correlators For Symmetric Double-Well Matrix Models: Some Puzzles and Resolutions

Details Smoothed Correlators For Symmetric Double-Well Matrix Models: Some Puzzles and Resolutions Smoothed Correlators For Symmetric Double-Well Matrix Models: Some Puzzles and Resolutions

1998-05-08

arxiv.org/abs/cond-mat/9805096v1

Physics

Condensed Matter

20 pages Latex, three postscript figures

Scientific paper

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 (OP) method. A few interesting observations are made regarding even and odd density-density correlators and cross-over correlators in $Z_2$ symmetric random matrix models.

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