  We investigate nonequilibrium energy transfer in a single-site Bose-Hubbard
model coupled to two thermal baths. By including a quantum kinetic equation
combined with full counting statistics, we investigate the steady state energy
flux and noise power. The influence of the nonlinear Bose-Hubbard interaction
on the transfer behaviors is analyzed, and the nonmonotonic features are
clearly exhibited. Particularly, in the strong on-site repulsion limit, the
results become identical with the nonequilibrium spin-boson model. We also
extend the quantum kinetic equation to study the geometric-phase-induced energy
pump. An interesting reversal behavior is unraveled by enhancing the
Bose-Hubbard repulsion strength.
