Volume 127, Number 3, August 2019
|Number of page(s)||7|
|Published online||12 September 2019|
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
Received: 16 May 2019
Accepted: 24 July 2019
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.
PACS: 05.45.Mt – Quantum chaos; semiclassical methods / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 03.65.Yz – Decoherence; open systems; quantum statistical methods
© EPLA, 2019
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