A Generalized Plasma and Interpolation Between Classical Random Matrix Ensembles
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The eigenvalue probability density functions of the classical random matrix ensembles have a well known analogy with the one component log-gas at the special couplings β=1,2 and 4. It has been known for some time that there is an exactly solvable two-component log-potential plasma which interpolates between the β=1 and 4 circular ensemble, and an exactly solvable two-component generalized plasma which interpolates between β=2 and 4 circular ensemble. We extend known exact results relating to the latter—for the free energy and one and two-point correlations—by giving the general (k 1+k 2)-point correlation function in a Pfaffian form. Crucial to our working is an identity which expresses the Vandermonde determinant in terms of a Pfaffian. The exact evaluation of the general correlation is used to exhibit a perfect screening sum rule.
KeywordsRandom matrix Generalized plasma Log-gas Pfaffian Two-point correlation Anomalous quantum Hall effect
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