  We study relaxation times, also called mixing times, of quantum many-body
systems described by a Lindblad master equation. We in particular study the
scaling of the spectral gap with the system length, the so-called dynamical
exponent, identifying a number of transitions in the scaling. For systems with
bulk dissipation we generically observe different scaling for small and for
strong dissipation strength, with a critical transition strength going to zero
in the thermodynamic limit. We also study a related phase transition in the
largest decay mode. For systems with only boundary dissipation we show a
generic bound that the gap can not be larger than 1/L. In integrable systems
with boundary dissipation one typically observes scaling 1/L^3, while in
chaotic ones one can have faster relaxation with the gap scaling as 1/L and
thus saturating the generic bound. We also observe transition from exponential
to algebraic gap in systems with localized modes.
