  We apply a new formalism to derive the higher-order quantum kinetic expansion
(QKE) for studying dissipative dynamics in a general quantum network coupled
with an arbitrary thermal bath. The dynamics of system population is described
by a time-convoluted kinetic equation, where the time-nonlocal rate kernel is
systematically expanded on the order of off-diagonal elements of the system
Hamiltonian. In the second order, the rate kernel recovers the expression of
the noninteracting-blip approximation (NIBA) method. The higher-order
corrections in the rate kernel account for the effects of the multi-site
quantum coherence and the bath relaxation. In a quantum harmonic bath, the rate
kernels of different orders are analytically derived. As demonstrated by four
examples, the higher-order QKE can reliably predict quantum dissipative
dynamics, comparing well with the hierarchic equation approach. More
importantly, the higher-order rate kernels can distinguish and quantify
distinct nontrivial quantum coherent effects, such as long-range energy
transfer from quantum tunneling and quantum interference arising from the phase
accumulation of interactions.
