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Open quantum systems with Markovian dynamics can be described by the Lindblad equation. The quantity governing the dynamics is the Lindblad superoperator. We apply random-matrix theory to this superoperator to elucidate its spectral properties. The distribution of eigenvalues and the correlations of neighboring eigenvalues are obtained for the cases of purely unitary dynamics, pure dissipation, and the physically realistic combination of unitary and dissipative dynamics.
The theory of ensembles of random matrices has proved useful in understanding the energy spectra of complex closed quantum systems, such as heavy atomic nuclei and classically chaotic billiards. In these cases, the Hamiltonian describing the system is drawn from a suitable random-matrix ensemble. More recently, it has been realized that random-matrix theory can also shed light on open quantum systems. Their dynamics is not described by a Hamiltonian but by a so-called Lindblad generator. Using random-matrix ensembles suitable for the Lindblad generator, we study its spectral properties, which are important for the dynamics of open quantum systems.
