Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices
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.
Cite
@article{arxiv.quant-ph/0209165,
title = {Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of random matrices},
author = {Zafar Ahmed and Sudhir R. Jain},
journal= {arXiv preprint arXiv:quant-ph/0209165},
year = {2009}
}
Comments
9 pages, 2 figures, LaTeX, submitted to the Physical Review Letters on August 20, 2002