ua nt - p h / 04 07 15 4 v 1 2 0 Ju l 2 00 4 Gaussian - random Ensembles of Pseudo - Hermitian Matrices ∗
نویسنده
چکیده
Attention has been brought to the possibility that statistical fluctuation properties of several complex spectra, or, well-known number sequences may display strong signatures that the Hamiltonian yielding them as eigenvalues is PT-symmetric (Pseudo-Hermitian). We find that the random matrix theory of pseudo-Hermitian Hamiltonians gives rise to new universalities of levelspacing distributions other than those of GOE, GUE and GSE of Wigner and Dyson. We call the new proposals as Gaussian Pseudo-Orthogonal Ensemble and Gaussian Pseudo-Unitary Ensemble. We are also led to speculate that the enigmatic Riemann-zeros (12 ± itn) would rather correspond to some PTsymmetric (pseudo-Hermitian) Hamiltonian.
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