Open quantum systems with Markovian dynamics can be described by the Lindblad equation. The quantity governing is superoperator. We apply random-matrix theory to this superoperator elucidate its spectral properties. distribution of eigenvalues and correlations neighboring are obtained for cases purely unitary dynamics, pure dissipation, physically realistic combination dissipative dynamics.

We investigate the local spectral statistics of loss surface Hessians artificial neural networks, where we discover excellent agreement with Gaussian Orthogonal Ensemble across several network architectures and datasets. These results shed new light on applicability Random Matrix Theory to modelling networks suggest a previously unrecognised role for it in study surfaces deep learning. Inspired...