Spectral and Steady-State Properties of Random Liouvillians. (arXiv:1905.02155v2 [quant-ph] UPDATED)

We study generic open quantum systems with Markovian dissipation, focusing on
a class of stochastic Liouvillian operators of Lindblad form with independent
random dissipation channels (jump operators) and a random Hamiltonian. We
establish that the global spectral features, the spectral gap, and the
steady-state properties follow three different regimes as a function of the
dissipation strength, whose boundaries depend on the particular observable.
Within each regime, we determine the scaling exponents with the dissipation
strength and system size. We find that, for two or more dissipation channels,
the spectral gap increases with the system size. The spectral distribution of
the steady-state is Poissonian at low dissipation strength and conforms to that
of a random matrix once the dissipation is sufficiently strong. Our results can
help to understand the long-time dynamics and steady-state properties of
generic dissipative systems.

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