Universality classes of quantum chaotic dissipative systems

¹ School of Physical Sciences, Jawaharlal Nehru University - New Delhi-110067, India
² Department of Physics, Indian Institute of Technology Madras - Chennai-600036, India

^(a) abjaiswal.jmi@gmail.com
^(b) ap0700@mail.jnu.ac.in
^(c) raviprakash.sps@gmail.com (corresponding author)

Received: 16 May 2019
Accepted: 24 July 2019

Abstract

We study the ensemble of complex symmetric matrices. The ensemble is useful in the study of the effect of dissipation on systems with time-reversal invariance. We consider the nearest-neighbor spacing distribution and spacing ratio to investigate the fluctuation statistics and show that these statistics are similar to that of dissipative chaotic systems with time-reversal invariance. We show that, unlike cubic repulsion in eigenvalues of Ginibre matrices, this ensemble exhibits a weaker repulsion. The nearest-neighbor spacing distribution exhibits for small spacings. We verify our results for quantum kicked rotor with time-reversal invariance. We show that the rotor exhibits similar spacing distribution in dissipative regime. We also discuss a random matrix model for transition from the time-reversal invariant to the broken case.