Gaussian ensemble of 2 × 2 pseudo-Hermitian random matrices

Authors: Ahmed Z.; Jain S.R.

Source: Journal of Physics A: Mathematical and General, Volume 36, Number 12, 2003 , pp. 3349-3362(14)

Publisher: Institute of Physics Publishing

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Abstract:

We 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.

Language: English

Document Type: Miscellaneous

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