PMID: 12786422Jun 6, 2003Paper

Pseudounitary symmetry and the Gaussian pseudounitary ensemble of random matrices

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Zafar Ahmed, Sudhir R Jain

Abstract

Employing the currently discussed notion of pseudo-Hermiticity, we define a pseudounitary group. Further, we develop a random matrix theory that is invariant under such a group and call this ensemble of pseudo-Hermitian random matrices the pseudounitary ensemble. We obtain exact results for the nearest-neighbor level-spacing distribution for (2 x 2) PT-invariant Hamiltonian matrices that have forms, approximately Sln(1/S) near zero spacing for three independent elements and approximately S for four independent elements. This shows a level repulsion in a marked distinction with an algebraic form S(beta) in the Wigner surmise. We believe that this paves the way for a description of varied phenomena in two-dimensional statistical mechanics, quantum chromodynamics, and so on.

References

Jan 1, 1995·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·G DateM V Murthy

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Citations

Jun 12, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Shashi C L Srivastava, Sudhir R Jain
Jan 20, 2018·Physical Review. E·G Marinello, M P Pato
Aug 31, 2016·Physical Review. E·G Marinello, M P Pato
Sep 28, 2017·Physical Review. E·Sachin Kumar, Zafar Ahmed
Nov 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·C MaleR Delannay
Oct 15, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sudhir R Jain, Shashi C L Srivastava
Oct 2, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tetsuo DeguchiKazue Kudo

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