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https://www.ias.ac.in/article/fulltext/pram/073/06/0989-0997

Random matrices; circulants; quantum chaos; $\mathcal{PT}$ symmetry; pseudo-Hermiticity.

We discuss the relevance of random matrix theory for pseudo-Hermitian systems, and, for Hamiltonians that break parity 𝑃 and time-reversal invariance 𝑇. In an attempt to understand the random Ising model, we present the treatment of cyclic asymmetric matrices with blocks and show that the nearest-neighbour spacing distributions have the same form as obtained for the matrices with scalar entries. We also summarize the theory for random cyclic matrices with scalar entries. We have also found that for block matrices made of Hermitian and pseudo-Hermitian sub-blocks of the form appearing in Ising model depart from the known results for scalar entries. However, there is still similarity in trends even in log–log plots.

Sudhir R Jain¹ Shashi C L Srivastava¹

1. Nuclear Physics Division, Van de Graaff Building, Bhabha Atomic Research Centre, Trombay, Mumbai 400 085, India

Published

December 2009

Manuscript received

18 April 2009

Manuscript revised

2 July 2009

Accepted

30 July 2009