Experimental investigation of distributions of the off-diagonal elements of the scattering matrix and Wigner's K[over ̂] matrix for networks with broken time reversal invariance.

We present an extensive experimental study of the distributions of the real and imaginary parts of the off-diagonal elements of the scattering matrix S[over ̂] and the Wigner's reaction K[over ̂] matrix for open microwave networks with broken time (T) reversal invariance. Microwave Faraday circulators were applied in order to break T invariance. The experimental distributions of the real and imaginary parts of the off-diagonal entries of the scattering matrix S[over ̂] are compared with the theoretical predictions from the supersymmetry random matrix theory [A. Nock, S. Kumar, H.-J. Sommers, and T. Guhr, Ann. Phys. (NY) 342, 103 (2014)10.1016/j.aop.2013.11.006]. Furthermore, we show that the experimental results are in very good agreement with the recent predictions for the distributions of the real and imaginary parts of the off-diagonal elements of the Wigner's reaction K[over ̂] matrix obtained within the framework of the Gaussian unitary ensemble of random matrix theory [S. B. Fedeli and Y. V. Fyodorov, J. Phys. A: Math. Theor. 53, 165701 (2020)1751-811310.1088/1751-8121/ab73ab]. Both theories include losses as tunable parameters and are therefore well adapted to the experimental verification.