Transition from Poisson to circular unitary ensemble

VINAYAK and AKHILESH PANDEY^*

School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110 067, India

^*Corresponding author

E-mail: vinayaksps2003@gmail.com; ap0700@mail.jnu.ac.in

Abstract. Transitions to universality classes of random matrix

ensembles have been useful in the study of weakly-broken symmetries

in quantum chaotic systems. Transitions involving Poisson as the

initial ensemble have been particularly interesting. The exact

two-point correlation function was derived by one of the present

authors for the Poisson to circular unitary ensemble (CUE)

transition with uniform initial density. This is given in terms of a

rescaled symmetry breaking parameter $\Lambda$. The same result was

obtained for Poisson to Gaussian unitary ensemble (GUE) transition

by Kunz and Shapiro, using the contour-integral method of Brezin and

Hikami. We show that their method is applicable to Poisson to CUE

transition with arbitrary initial density. Their method is also

applicable to the more general $\ell$CUE to CUE transition where

$\ell$CUE refers to the superposition of $\ell$ independent CUE

spectra in arbitrary ratio.

Keywords. Quantum chaos; random matrix; symmetry breaking;

fluctuations; correlation functions; Brownian motion; contour

integral.

PACS Nos 5.45.Mt; 24.60.Lz; 73.23.-b; 3.65.-w