  We analytically investigate the non-equilibrium pumping for a double quantum
dots system on the basis of the quantum master equation (QME), where the double
quantum dots are connected to two external leads by the spin coupling. Each of
leads has two tunable parameters, temperature and chemical potential. Using QME
formalism, we obtain an analytical expression of the Berry-like phase for
eigenstate of the QME in the parameter space. We show that the Berry-like
curvature is non zero in the whole region in the parameter space. We also show
that the Berry-like curvature vanishes in the case of single quantum dot and
the case of isolated two dots.
