Physics – Quantum Physics
Scientific paper
2002-09-30
Physics
Quantum Physics
9 pages, 2 figures, LaTeX, submitted to the Physical Review Letters on August 20, 2002
Scientific paper
10.1103/PhysRevE.67.045106
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.
Ahmed Zafar
Jain Sudhir R.
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