Zafar Ahmed and Sudhir R Jain 2003 J. Phys. A: Math. Gen. 36 3349 doi:10.1088/0305-4470/36/12/327
Gaussian ensemble of 2 × 2 pseudo-Hermitian random matrices
Zafar Ahmed and Sudhir R Jain
Show affiliationsWe present a random matrix theory for systems invariant under the joint action of parity, 
, and time reversal, 
, and, more generally, for pseudo-Hermitian systems. This brings out the appearance of the metric in a systematic way so that consistency with the postulates of quantum mechanics is maintained. Here we specialize only to 2 × 2 matrices and we construct a pseudo-unitary group. With explicit examples, nearest-neighbour level-spacing distributions for various classes of ensembles are found to exhibit a degree of level repulsion different from those hitherto known. This work is not only relevant to quantum chaos, but also to two-dimensional statistical mechanics and consistent non-local relativistic theories.
- PACS
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05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion
- MSC
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15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)
- Subjects
- Dates
-
Issue 12 (28 March 2003)
Received 2 September 2002, in final form 7 February 2003
Published 12 March 2003
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Gaussian ensemble of 2 × 2 pseudo-Hermitian random matrices
Zafar Ahmed and Sudhir R Jain 2003 J. Phys. A: Math. Gen. 36 3349
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Preface
J F Benage, J W Dufty and M S Murillo 2003 J. Phys. A: Math. Gen. 36
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