Embedded Random Matrix Ensembles in Quantum Physics by V.K.B. Kota

Author:V.K.B. Kota
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

The EGOE(1+2)-π ensemble is defined by choosing the matrices A, B and C to be independent GOEs with matrix elements variances , and respectively [2]. Similarly, matrix elements of the mixing D matrix are chosen to be independent (independent of A, B and C matrix elements) zero centered Gaussian variables with variance . Without loss of generality we choose Δ=1 so that all the v’s are in Δ units. This general EGOE(1+2)-π model will have too many parameters () and therefore it is necessary to reduce the number of parameters. A numerically tractable and physically relevant (as discussed ahead) restriction is to choose the matrix elements variances of the diagonal blocks A, B and C to be same and then we have the EGOE(1+2)-π model defined by (N +,N −,m) and the variance parameters (τ,α) where

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