Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2005-04-04
Physics
Condensed Matter
Other Condensed Matter
4 pages, to be published in Phys. Rev. E, Rapid Comm
Scientific paper
10.1103/PhysRevE.71.055101
We construct a very general family of characteristic functions describing Random Matrix Ensembles (RME) having a global unitary invariance, and containing an arbitrary, one-variable probability measure which we characterize by a `spread function'. Various choices of the spread function lead to a variety of possible generalized RMEs, which show deviations from the well-known Gaussian RME originally proposed by Wigner. We obtain the correlation functions of such generalized ensembles exactly, and show examples of how particular choices of the spread function can describe ensembles with arbitrary eigenvalue densities as well as critical ensembles with multifractality.
Klauder John R.
Muttalib Khandker A.
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