The joint energy distribution function for the Hamiltonian for the one-channel case

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Abstract
A closed analytical expression is derived for the joint distribution function of the real and the imaginary parts of the eigenenergies of the operator for the one-channel case, where is taken from the Poissonian or one of the Gaussian ensembles with universality index , and where the squared moduli of the components of W are assumed to be -distributed with universality index . In the strong coupling limit and for the special case the joint distribution function of the real parts of the eigenvalues of H becomes identical with the joint energy distribution function of the eigenvalues of .