Physics – Condensed Matter
Scientific paper
1997-04-17
Philosophical Magazine B 77, 1161 (1998)
Physics
Condensed Matter
13 pages (latex), Presented at the MINERVA Workshop on Mesoscopics, Fractals and Neural Networks, Eilat, Israel, March 1997
Scientific paper
Joint distribution function of N eigenvalues of U(N) invariant random-matrix ensemble can be interpreted as a probability density to find N fictitious non-interacting fermions to be confined in a one-dimensional space. Within this picture a general formalism is developed to study the eigenvalue correlations in non-Gaussian ensembles of large random matrices possessing non-monotonic, log-singular level confinement. An effective one-particle Schroedinger equation for wave-functions of fictitious fermions is derived. It is shown that eigenvalue correlations are completely determined by the Dyson's density of states and by the parameter of the logarithmic singularity. Closed analytical expressions for the two-point kernel in the origin, bulk, and soft-edge scaling limits are deduced in a unified way, and novel universal correlations are predicted near the end point of the single spectrum support.
Freilikher Valentin
Kanzieper Eugene
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