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.
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