Universal spectral correlations in ensembles of random normal matrices
School of Physical Sciences, Jawaharlal Nehru University - New Delhi - 110067, India
Received: 11 November 2014
Accepted: 20 April 2015
We consider non-Gaussian ensembles of random normal matrices with the constraint that the ensembles are invariant under unitary transformations. We show that the level density of eigenvalues exhibits disk or ring structure in the complex plane. We also show that the n-eigenvalue correlation and the spacing distribution are universal and identical to that of complex (Gaussian) Ginibre ensemble. Our results are confirmed by Monte Carlo calculations. We verify the universality for dissipative quantum kicked rotor systems.
PACS: 05.45.Mt – Quantum chaos; semiclassical methods / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.Ng – Distribution theory and Monte Carlo studies
© EPLA, 2015