Universality in Chiral Random Matrix Theory at {beta} = 1 and {beta} = 4
- Department of Physics and Astronomy, SUNY, Stony Brook, New York 11794 (United States)
In this paper the kernel for the spectral correlation functions of invariant chiral random matrix ensembles with real ({beta}=1 ) and quaternion real ({beta}=4 ) matrix elements is expressed in terms of the kernel of the corresponding complex Hermitian random matrix ensembles ({beta}=2 ). Such identities are exact in case of a Gaussian probability distribution and, under certain smoothness assumptions, they are shown to be valid asymptotically for an arbitrary finite polynomial potential. They are proved by means of a construction proposed by Brezin and Neuberger. Universal behavior of the eigenvalues close to zero for all three chiral ensembles then follows from microscopic universality for {beta}=2 as shown by Akemann, Damgaard, Magnea, and Nishigaki. {copyright} {ital 1998} {ital The American Physical Society}
- Research Organization:
- New York State University Research Foundation
- DOE Contract Number:
- FG02-88ER40388
- OSTI ID:
- 664998
- Journal Information:
- Physical Review Letters, Vol. 81, Issue 2; Other Information: PBD: Jul 1998
- Country of Publication:
- United States
- Language:
- English
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