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Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices

Zafar Ahmed·Sudhir R. Jain
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Abstract

Employing the currently discussed notion of pseudo-Hermiticity, we define a pseudo-unitary group. Further, we develop a random matrix theory which is invariant under such a group and call this ensemble of pseudo-Hermitian random matrices as the pseudo-unitary ensemble. We obtain exact results for the nearest-neighbour level spacing distribution for (2 X 2) PT-symmetric Hamiltonian matrices which has a novel form, s log (1/s) near zero spacing. This shows a level repulsion in marked distinction with an algebraic form in the Wigner surmise. We believe that this paves way for a description of varied phenomena in two-dimensional statistical mechanics, quantum chromodynamics, and so on.

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Zafar Ahmed, Sudhir R. Jain. 2002-09-30. Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices. https://doi.org/10.1103/physreve.67.045106

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