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We clarify the role of non-adiabatic effects in a quantum pumping for aspin-boson system. When we sinusoidally control the temperatures of tworeservoirs with \pi/2 phase difference, we find that the pumping currentstrongly depends on the initial condition, and thus, the current deviates fromthat predicted by the adiabatic treatment. We also analytically obtain thecontribution of non-adiabatic effects in the pumping current proportional to\Omega^3 where \Omega is the angular frequency of the temperature control. Thevalidity of the analytic expression is verified by our numerical calculation.Moreover, we extend the steady heat fluctuation theorem to the case for slowlymodulated temperatures and large transferred energies.

Non-adiabatic effect in quantum pumping for a spin-boson system