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

E. Brezin; N. Deo

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arXiv · cond-mat/9805096

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

E. Brezin·N. Deo

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Abstract

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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E. Brezin, N. Deo. 1998-05-08. Smoothed Correlators For Symmetric Double-Well Matrix Models: Some Puzzles and Resolutions. https://arxiv.org/abs/cond-mat/9805096

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