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Dyson-Schwinger loop equations of the two-matrix model: Eigenvalue Correlations in quantum chaos

Deo, Nivedita and Jain, Sanjay and Shastry, Sriram B (1995) Dyson-Schwinger loop equations of the two-matrix model: Eigenvalue Correlations in quantum chaos. In: physical Review Online Archive, 52 (5). 4836 -4840.

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Abstract

We determine a set of Dyson-Schwinger equations or loop equations for a model of two coupled random matrices belonging to the orthogonal, unitary, or symplectic ensembles. In the large N limit, the loop equations become closed algebraic equations, allowing us to obtain the correlations between the eigenvalues of the two matrices. The expression we obtain is valid near the center as well as the edge of the cut. In particular, this determines how the correlations between the eigenvalues of perturbed and unperturbed chaotic Hamiltonians depend upon the strength of the perturbation, and also the space and time dependence of density-density correlators of the Calogero-Sutherland-Moser model for three values of the coupling constant.

Item Type: Journal Article
Additional Information: Copyright belongs to The American Physical Society.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for Theoretical Studies
Division of Physical & Mathematical Sciences > Physics
Date Deposited: 13 Jun 2008
Last Modified: 19 Sep 2010 04:45
URI: http://eprints.iisc.ernet.in/id/eprint/14324

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