In dissipative bosonic systems, dephasing is typically expected to accelerate
relaxation and suppress coherent dynamics. However, we show that in
networks of coherently coupled bosonic modes with non-uniform local
dissipation, the presence of quasi-dark states leads to a nontrivial response
to dephasing: while weak dephasing facilitates equilibration, moderate to
strong dephasing induces a pronounced slowdown of relaxation, revealing
the existence of an optimal dephasing rate that enhances equilibration.
Using exact dynamical equations for second-order moments, we demonstrate
that dephasing suppresses coherent transport and gives rise to longlived
collective modes that dominate the system’s late-time behavior. This
phenomenon bears striking similarities to Lifshitz-tail states, which are
known in disordered systems to cause anomalously slow relaxation. Our
results uncover a counterintuitive mechanism by which dephasing, rather
than promoting equilibration, can dynamically decouple specific modes
from dissipation, thereby protecting excitations. These findings highlight
how non-Hermitian physics in open bosonic systems can give rise to unexpected
dynamical regimes, paving the way for new strategies to control
relaxation and decoherence in bosonic quantum systems, with broad
implications for both experimental and theoretical quantum science.