  Open quantum systems with nearly degenerate energy levels have been shown to
exhibit long-lived metastable states in the approach to equilibrium, even when
modelled with certain Lindblad-form quantum master equations. This is a result
of dramatic separation of timescales due to differences between Liouvillian
eigenvalues. These metastable states often have nonzero coherences which die
off only in the long time limit once the system reaches thermal equilibrium. We
examine two distinct situations that give rise to this effect: one in which
dissipative dynamics couple together states only within a nearly degenerate
subspace, and one in which they give rise to jumps over finite energy
splittings, between separate nearly degenerate subspaces. We find, in each
case, that a change of basis can often lead to a representation which more
naturally captures the impact of the system-bath interaction than does the
energy eigenbasis, revealing that separate timescales are associated with
separate processes (e.g. decoherence into a non-energy eigenbasis, decay of
population correlations to the initial state). This approach is paired with the
inspection of quantum trajectories, which further provide intuition as to how
open system evolution is characterized when coherent oscillations, thermal
relaxation, and decoherence all occur simultaneously.
