Random Lindblad Dynamics*

The Lindblad superoperator is the generator of time translation for the quantum Markov master equation. We ask the question: what dynamics follow from a random Lindblad generator? To answer this, we define an ensemble of Lindblad superoperators using random matrix theory, and study the statistical properties its eigenvalues. In particular, we characterize the spectral gap (a.k.a. dissipative gap) which determines the asymptotic decay rate of typical operators in the Hilbert space. We find that the spectral gap is finite in the limit of infinite Hilbert space dimension, and described by a universal non-monotonic scaling function of the dissipative coupling constant.