  Understanding non-equilibrium heat transport is crucial for controling heat
flow in nano-scale systems. We study thermal energy transfer in a generalized
non-equilibrium spin-boson model (NESB) with non-commutative system-bath
coupling operators and discover unusual transport properties. Compared to the
conventional NESB, the heat current is greatly enhanced by rotating the
coupling operators. Constructive contribution to thermal rectification can be
optimized when two sources of asymmetry, system-bath coupling strength and
coupling operators, coexist. At the weak coupling and the adiabatic limit, the
scaling dependence of heat current on the coupling strength and the system
energy gap changes drastically when the coupling operators become
non-commutative. These scaling relations can further be explained analytically
by the non-equilibrium polaron-transformed Redfield equation. These novel
transport properties, arising from the pure quantum effect of non-commutative
coupling operators, should generally appear in other non-equilibrium set-ups
and driven-systems.
