Analytical expression of geometrical pumping for a quantum dot based on quantum master equation

We analytically investigate a non-equilibrium quantum pumping for a single quantum dot connected to external leads on the basis of the quantum master equation (QME). We show that the Coulomb interaction associated with the spin effect in the dot induces the Berry-like phase in the parameter space and this phase results in the excess charge transfer for the cyclic modulation of parameters in leads. We obtain an analytical expression of the curvature of the phase and that for the pumped currents.